Seconde - Calculer les coordonnées d'un vecteur

Calculer les coordonnées d'un vecteur

Episode 2

🔑 Pour suivre cet épisode tu dois :

avoir regardé l'épisode 1 ;
avoir cherché sur papier l'exercice de la fin de l'épisode.

📝 Résumé de l'épisode :

Nous donnons les solutions détaillées de l'exercice d'entraînement qui a terminé l'épisode 1.

1. $\overrightarrow{\mathrm{FT}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{2} ;\htmlData{state=on,id=e6}{-7}\right)$ et $\mathrm{T}\left(\htmlData{state=on,id=e1}{3} ; \htmlData{state=on,id=e4}{7}\right)$.

$\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{T}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{T}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=off,id=e1}{3}\htmlData{state=off,id=e2}{-}\htmlData{state=off,id=e3}{2}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{7}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-7)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=off,id=e9}{1}\\ \htmlData{state=off,id=e8}{14} \end{pmatrix}$

Voici la formule qui permet de calculer les coordonnées de $\overrightarrow{\mathrm{FT}}$

1. $\overrightarrow{\mathrm{FT}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{2} ;\htmlData{state=on,id=e6}{-7}\right)$ et $\mathrm{T}\left(\htmlData{state=on,id=e1}{3} ; \htmlData{state=on,id=e4}{7}\right)$.

$\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{T}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{T}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=off,id=e1}{3}\htmlData{state=off,id=e2}{-}\htmlData{state=off,id=e3}{2}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{7}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-7)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=off,id=e9}{1}\\ \htmlData{state=off,id=e8}{14} \end{pmatrix}$

Appliquons cette formule.

1. $\overrightarrow{\mathrm{FT}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{2} ;\htmlData{state=on,id=e6}{-7}\right)$ et $\mathrm{T}\left(\htmlData{state=hl,id=e1}{3} ; \htmlData{state=on,id=e4}{7}\right)$.

$\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=hl,id=e1}{x_\mathrm{T}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{T}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=hl,id=e1}{3}\htmlData{state=off,id=e2}{-}\htmlData{state=off,id=e3}{2}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{7}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-7)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=off,id=e9}{1}\\ \htmlData{state=off,id=e8}{14} \end{pmatrix}$

Le nombre $x_\mathrm{T}$ est l'abscisse du point $\mathrm{T}$, c'est $3$.

1. $\overrightarrow{\mathrm{FT}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{2} ;\htmlData{state=on,id=e6}{-7}\right)$ et $\mathrm{T}\left(\htmlData{state=on,id=e1}{3} ; \htmlData{state=on,id=e4}{7}\right)$.

$\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{T}}\htmlData{state=hl,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{T}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{3}\htmlData{state=hl,id=e2}{-}\htmlData{state=off,id=e3}{2}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{7}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-7)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=off,id=e9}{1}\\ \htmlData{state=off,id=e8}{14} \end{pmatrix}$

moins ...

1. $\overrightarrow{\mathrm{FT}}$ avec $\mathrm{F}\left(\htmlData{state=hl,id=e3}{2} ;\htmlData{state=on,id=e6}{-7}\right)$ et $\mathrm{T}\left(\htmlData{state=on,id=e1}{3} ; \htmlData{state=on,id=e4}{7}\right)$.

$\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{T}}\htmlData{state=on,id=e2}{-}\htmlData{state=hl,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{T}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{3}\htmlData{state=on,id=e2}{-}\htmlData{state=hl,id=e3}{2}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{7}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-7)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=off,id=e9}{1}\\ \htmlData{state=off,id=e8}{14} \end{pmatrix}$

Le nombre $x_\mathrm{F}$ est l'abscisse du point $\mathrm{F}$, c'est $2$.

1. $\overrightarrow{\mathrm{FT}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{2} ;\htmlData{state=on,id=e6}{-7}\right)$ et $\mathrm{T}\left(\htmlData{state=on,id=e1}{3} ; \htmlData{state=hl,id=e4}{7}\right)$.

$\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{T}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=hl,id=e4}{y_\mathrm{T}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{3}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{2}}\\ \htmlData{state=on,id=e8}{\htmlData{state=hl,id=e4}{7}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-7)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=off,id=e9}{1}\\ \htmlData{state=off,id=e8}{14} \end{pmatrix}$

Le nombre $y_\mathrm{T}$ est l'ordonnée du point $\mathrm{T}$, c'est $7$.

1. $\overrightarrow{\mathrm{FT}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{2} ;\htmlData{state=on,id=e6}{-7}\right)$ et $\mathrm{T}\left(\htmlData{state=on,id=e1}{3} ; \htmlData{state=on,id=e4}{7}\right)$.

$\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{T}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{T}}\htmlData{state=hl,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{3}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{2}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{7}\htmlData{state=hl,id=e5}{-}\htmlData{state=off,id=e6}{(-7)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=off,id=e9}{1}\\ \htmlData{state=off,id=e8}{14} \end{pmatrix}$

moins ...

1. $\overrightarrow{\mathrm{FT}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{2} ;\htmlData{state=hl,id=e6}{-7}\right)$ et $\mathrm{T}\left(\htmlData{state=on,id=e1}{3} ; \htmlData{state=on,id=e4}{7}\right)$.

$\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{T}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{T}}\htmlData{state=on,id=e5}{-}\htmlData{state=hl,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{3}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{2}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{7}\htmlData{state=on,id=e5}{-}\htmlData{state=hl,id=e6}{(-7)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=off,id=e9}{1}\\ \htmlData{state=off,id=e8}{14} \end{pmatrix}$

Le nombre $y_\mathrm{F}$ est l'ordonnée du point $\mathrm{F}$, c'est $-7$.

1. $\overrightarrow{\mathrm{FT}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{2} ;\htmlData{state=on,id=e6}{-7}\right)$ et $\mathrm{T}\left(\htmlData{state=on,id=e1}{3} ; \htmlData{state=on,id=e4}{7}\right)$.

$\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{T}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{T}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{3}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{2}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{7}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{(-7)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=off,id=e9}{1}\\ \htmlData{state=off,id=e8}{14} \end{pmatrix}$

On effectue les calculs.

1. $\overrightarrow{\mathrm{FT}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{2} ;\htmlData{state=on,id=e6}{-7}\right)$ et $\mathrm{T}\left(\htmlData{state=on,id=e1}{3} ; \htmlData{state=on,id=e4}{7}\right)$.

$\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{T}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{T}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=hl,id=e9}{\htmlData{state=on,id=e1}{3}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{2}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{7}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{(-7)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=hl,id=e9}{1}\\ \htmlData{state=off,id=e8}{14} \end{pmatrix}$

$3-2=1$

1. $\overrightarrow{\mathrm{FT}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{2} ;\htmlData{state=on,id=e6}{-7}\right)$ et $\mathrm{T}\left(\htmlData{state=on,id=e1}{3} ; \htmlData{state=on,id=e4}{7}\right)$.

$\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{T}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{T}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{3}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{2}}\\ \htmlData{state=hl,id=e8}{\htmlData{state=on,id=e4}{7}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{(-7)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e9}{1}\\ \htmlData{state=hl,id=e8}{14} \end{pmatrix}$

$7-\left(-7\right)=7+7=14$

1. $\overrightarrow{\mathrm{FT}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{2} ;\htmlData{state=on,id=e6}{-7}\right)$ et $\mathrm{T}\left(\htmlData{state=on,id=e1}{3} ; \htmlData{state=on,id=e4}{7}\right)$.

$\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{T}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{T}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{3}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{2}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{7}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{(-7)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FT}}\begin{pmatrix} \htmlData{state=on,id=e9}{1}\\ \htmlData{state=on,id=e8}{14} \end{pmatrix}$

2. $\overrightarrow{\mathrm{PE}}$ avec $\mathrm{P}\left(\htmlData{state=on,id=e3}{9} ;\htmlData{state=on,id=e6}{-5}\right)$ et $\mathrm{E}\left(\htmlData{state=on,id=e1}{4} ; \htmlData{state=on,id=e4}{1}\right)$.

$\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{E}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{P}}\\ \htmlData{state=on,id=e4}{y_\mathrm{E}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{P}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=off,id=e1}{4}\htmlData{state=off,id=e2}{-}\htmlData{state=off,id=e3}{9}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{1}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-5)}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=off,id=e9}{-5}\\ \htmlData{state=off,id=e8}{6} \end{pmatrix}$

Voici la formule qui permet de calculer les coordonnées de $\overrightarrow{\mathrm{PE}}$

2. $\overrightarrow{\mathrm{PE}}$ avec $\mathrm{P}\left(\htmlData{state=on,id=e3}{9} ;\htmlData{state=on,id=e6}{-5}\right)$ et $\mathrm{E}\left(\htmlData{state=on,id=e1}{4} ; \htmlData{state=on,id=e4}{1}\right)$.

$\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{E}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{P}}\\ \htmlData{state=on,id=e4}{y_\mathrm{E}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{P}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=off,id=e1}{4}\htmlData{state=off,id=e2}{-}\htmlData{state=off,id=e3}{9}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{1}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-5)}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=off,id=e9}{-5}\\ \htmlData{state=off,id=e8}{6} \end{pmatrix}$

Appliquons cette formule.

2. $\overrightarrow{\mathrm{PE}}$ avec $\mathrm{P}\left(\htmlData{state=on,id=e3}{9} ;\htmlData{state=on,id=e6}{-5}\right)$ et $\mathrm{E}\left(\htmlData{state=hl,id=e1}{4} ; \htmlData{state=on,id=e4}{1}\right)$.

$\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=hl,id=e1}{x_\mathrm{E}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{P}}\\ \htmlData{state=on,id=e4}{y_\mathrm{E}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{P}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=hl,id=e1}{4}\htmlData{state=off,id=e2}{-}\htmlData{state=off,id=e3}{9}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{1}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-5)}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=off,id=e9}{-5}\\ \htmlData{state=off,id=e8}{6} \end{pmatrix}$

Le nombre $x_\mathrm{E}$ est l'abscisse du point $\mathrm{E}$, c'est $4$.

2. $\overrightarrow{\mathrm{PE}}$ avec $\mathrm{P}\left(\htmlData{state=on,id=e3}{9} ;\htmlData{state=on,id=e6}{-5}\right)$ et $\mathrm{E}\left(\htmlData{state=on,id=e1}{4} ; \htmlData{state=on,id=e4}{1}\right)$.

$\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{E}}\htmlData{state=hl,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{P}}\\ \htmlData{state=on,id=e4}{y_\mathrm{E}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{P}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{4}\htmlData{state=hl,id=e2}{-}\htmlData{state=off,id=e3}{9}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{1}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-5)}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=off,id=e9}{-5}\\ \htmlData{state=off,id=e8}{6} \end{pmatrix}$

moins ...

2. $\overrightarrow{\mathrm{PE}}$ avec $\mathrm{P}\left(\htmlData{state=hl,id=e3}{9} ;\htmlData{state=on,id=e6}{-5}\right)$ et $\mathrm{E}\left(\htmlData{state=on,id=e1}{4} ; \htmlData{state=on,id=e4}{1}\right)$.

$\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{E}}\htmlData{state=on,id=e2}{-}\htmlData{state=hl,id=e3}{x_\mathrm{P}}\\ \htmlData{state=on,id=e4}{y_\mathrm{E}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{P}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{4}\htmlData{state=on,id=e2}{-}\htmlData{state=hl,id=e3}{9}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{1}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-5)}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=off,id=e9}{-5}\\ \htmlData{state=off,id=e8}{6} \end{pmatrix}$

Le nombre $x_\mathrm{P}$ est l'abscisse du point $\mathrm{P}$, c'est $9$.

2. $\overrightarrow{\mathrm{PE}}$ avec $\mathrm{P}\left(\htmlData{state=on,id=e3}{9} ;\htmlData{state=on,id=e6}{-5}\right)$ et $\mathrm{E}\left(\htmlData{state=on,id=e1}{4} ; \htmlData{state=hl,id=e4}{1}\right)$.

$\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{E}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{P}}\\ \htmlData{state=hl,id=e4}{y_\mathrm{E}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{P}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{4}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{9}}\\ \htmlData{state=on,id=e8}{\htmlData{state=hl,id=e4}{1}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-5)}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=off,id=e9}{-5}\\ \htmlData{state=off,id=e8}{6} \end{pmatrix}$

Le nombre $y_\mathrm{E}$ est l'ordonnée du point $\mathrm{E}$, c'est $1$.

2. $\overrightarrow{\mathrm{PE}}$ avec $\mathrm{P}\left(\htmlData{state=on,id=e3}{9} ;\htmlData{state=on,id=e6}{-5}\right)$ et $\mathrm{E}\left(\htmlData{state=on,id=e1}{4} ; \htmlData{state=on,id=e4}{1}\right)$.

$\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{E}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{P}}\\ \htmlData{state=on,id=e4}{y_\mathrm{E}}\htmlData{state=hl,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{P}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{4}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{9}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{1}\htmlData{state=hl,id=e5}{-}\htmlData{state=off,id=e6}{(-5)}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=off,id=e9}{-5}\\ \htmlData{state=off,id=e8}{6} \end{pmatrix}$

moins ...

2. $\overrightarrow{\mathrm{PE}}$ avec $\mathrm{P}\left(\htmlData{state=on,id=e3}{9} ;\htmlData{state=hl,id=e6}{-5}\right)$ et $\mathrm{E}\left(\htmlData{state=on,id=e1}{4} ; \htmlData{state=on,id=e4}{1}\right)$.

$\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{E}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{P}}\\ \htmlData{state=on,id=e4}{y_\mathrm{E}}\htmlData{state=on,id=e5}{-}\htmlData{state=hl,id=e6}{y_\mathrm{P}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{4}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{9}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{1}\htmlData{state=on,id=e5}{-}\htmlData{state=hl,id=e6}{(-5)}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=off,id=e9}{-5}\\ \htmlData{state=off,id=e8}{6} \end{pmatrix}$

Le nombre $y_\mathrm{P}$ est l'ordonnée du point $\mathrm{P}$, c'est $-5$.

2. $\overrightarrow{\mathrm{PE}}$ avec $\mathrm{P}\left(\htmlData{state=on,id=e3}{9} ;\htmlData{state=on,id=e6}{-5}\right)$ et $\mathrm{E}\left(\htmlData{state=on,id=e1}{4} ; \htmlData{state=on,id=e4}{1}\right)$.

$\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{E}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{P}}\\ \htmlData{state=on,id=e4}{y_\mathrm{E}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{P}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{4}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{9}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{1}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{(-5)}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=off,id=e9}{-5}\\ \htmlData{state=off,id=e8}{6} \end{pmatrix}$

On effectue les calculs.

2. $\overrightarrow{\mathrm{PE}}$ avec $\mathrm{P}\left(\htmlData{state=on,id=e3}{9} ;\htmlData{state=on,id=e6}{-5}\right)$ et $\mathrm{E}\left(\htmlData{state=on,id=e1}{4} ; \htmlData{state=on,id=e4}{1}\right)$.

$\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{E}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{P}}\\ \htmlData{state=on,id=e4}{y_\mathrm{E}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{P}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=hl,id=e9}{\htmlData{state=on,id=e1}{4}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{9}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{1}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{(-5)}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=hl,id=e9}{-5}\\ \htmlData{state=off,id=e8}{6} \end{pmatrix}$

$4-9=-5$

2. $\overrightarrow{\mathrm{PE}}$ avec $\mathrm{P}\left(\htmlData{state=on,id=e3}{9} ;\htmlData{state=on,id=e6}{-5}\right)$ et $\mathrm{E}\left(\htmlData{state=on,id=e1}{4} ; \htmlData{state=on,id=e4}{1}\right)$.

$\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{E}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{P}}\\ \htmlData{state=on,id=e4}{y_\mathrm{E}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{P}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{4}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{9}}\\ \htmlData{state=hl,id=e8}{\htmlData{state=on,id=e4}{1}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{(-5)}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e9}{-5}\\ \htmlData{state=hl,id=e8}{6} \end{pmatrix}$

$1-\left(-5\right)=1+5=6$

2. $\overrightarrow{\mathrm{PE}}$ avec $\mathrm{P}\left(\htmlData{state=on,id=e3}{9} ;\htmlData{state=on,id=e6}{-5}\right)$ et $\mathrm{E}\left(\htmlData{state=on,id=e1}{4} ; \htmlData{state=on,id=e4}{1}\right)$.

$\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{E}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{P}}\\ \htmlData{state=on,id=e4}{y_\mathrm{E}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{P}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{4}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{9}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{1}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{(-5)}} \end{pmatrix}$ $\overrightarrow{\mathrm{PE}}\begin{pmatrix} \htmlData{state=on,id=e9}{-5}\\ \htmlData{state=on,id=e8}{6} \end{pmatrix}$

3. $\overrightarrow{\mathrm{ED}}$ avec $\mathrm{E}\left(\htmlData{state=on,id=e3}{-8} ;\htmlData{state=on,id=e6}{6}\right)$ et $\mathrm{D}\left(\htmlData{state=on,id=e1}{-2} ; \htmlData{state=on,id=e4}{2}\right)$.

$\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{D}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{E}}\\ \htmlData{state=on,id=e4}{y_\mathrm{D}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{E}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=off,id=e1}{-2}\htmlData{state=off,id=e2}{-}\htmlData{state=off,id=e3}{(-8)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{2}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{6}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=off,id=e9}{6}\\ \htmlData{state=off,id=e8}{-4} \end{pmatrix}$

Voici la formule qui permet de calculer les coordonnées de $\overrightarrow{\mathrm{ED}}$

3. $\overrightarrow{\mathrm{ED}}$ avec $\mathrm{E}\left(\htmlData{state=on,id=e3}{-8} ;\htmlData{state=on,id=e6}{6}\right)$ et $\mathrm{D}\left(\htmlData{state=on,id=e1}{-2} ; \htmlData{state=on,id=e4}{2}\right)$.

$\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{D}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{E}}\\ \htmlData{state=on,id=e4}{y_\mathrm{D}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{E}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=off,id=e1}{-2}\htmlData{state=off,id=e2}{-}\htmlData{state=off,id=e3}{(-8)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{2}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{6}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=off,id=e9}{6}\\ \htmlData{state=off,id=e8}{-4} \end{pmatrix}$

Appliquons cette formule.

3. $\overrightarrow{\mathrm{ED}}$ avec $\mathrm{E}\left(\htmlData{state=on,id=e3}{-8} ;\htmlData{state=on,id=e6}{6}\right)$ et $\mathrm{D}\left(\htmlData{state=hl,id=e1}{-2} ; \htmlData{state=on,id=e4}{2}\right)$.

$\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=hl,id=e1}{x_\mathrm{D}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{E}}\\ \htmlData{state=on,id=e4}{y_\mathrm{D}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{E}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=hl,id=e1}{-2}\htmlData{state=off,id=e2}{-}\htmlData{state=off,id=e3}{(-8)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{2}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{6}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=off,id=e9}{6}\\ \htmlData{state=off,id=e8}{-4} \end{pmatrix}$

Le nombre $x_\mathrm{D}$ est l'abscisse du point $\mathrm{D}$, c'est $-2$.

3. $\overrightarrow{\mathrm{ED}}$ avec $\mathrm{E}\left(\htmlData{state=on,id=e3}{-8} ;\htmlData{state=on,id=e6}{6}\right)$ et $\mathrm{D}\left(\htmlData{state=on,id=e1}{-2} ; \htmlData{state=on,id=e4}{2}\right)$.

$\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{D}}\htmlData{state=hl,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{E}}\\ \htmlData{state=on,id=e4}{y_\mathrm{D}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{E}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-2}\htmlData{state=hl,id=e2}{-}\htmlData{state=off,id=e3}{(-8)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{2}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{6}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=off,id=e9}{6}\\ \htmlData{state=off,id=e8}{-4} \end{pmatrix}$

moins ...

3. $\overrightarrow{\mathrm{ED}}$ avec $\mathrm{E}\left(\htmlData{state=hl,id=e3}{-8} ;\htmlData{state=on,id=e6}{6}\right)$ et $\mathrm{D}\left(\htmlData{state=on,id=e1}{-2} ; \htmlData{state=on,id=e4}{2}\right)$.

$\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{D}}\htmlData{state=on,id=e2}{-}\htmlData{state=hl,id=e3}{x_\mathrm{E}}\\ \htmlData{state=on,id=e4}{y_\mathrm{D}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{E}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-2}\htmlData{state=on,id=e2}{-}\htmlData{state=hl,id=e3}{(-8)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{2}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{6}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=off,id=e9}{6}\\ \htmlData{state=off,id=e8}{-4} \end{pmatrix}$

Le nombre $x_\mathrm{E}$ est l'abscisse du point $\mathrm{E}$, c'est $-8$.

3. $\overrightarrow{\mathrm{ED}}$ avec $\mathrm{E}\left(\htmlData{state=on,id=e3}{-8} ;\htmlData{state=on,id=e6}{6}\right)$ et $\mathrm{D}\left(\htmlData{state=on,id=e1}{-2} ; \htmlData{state=hl,id=e4}{2}\right)$.

$\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{D}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{E}}\\ \htmlData{state=hl,id=e4}{y_\mathrm{D}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{E}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-2}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-8)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=hl,id=e4}{2}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{6}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=off,id=e9}{6}\\ \htmlData{state=off,id=e8}{-4} \end{pmatrix}$

Le nombre $y_\mathrm{D}$ est l'ordonnée du point $\mathrm{D}$, c'est $2$.

3. $\overrightarrow{\mathrm{ED}}$ avec $\mathrm{E}\left(\htmlData{state=on,id=e3}{-8} ;\htmlData{state=on,id=e6}{6}\right)$ et $\mathrm{D}\left(\htmlData{state=on,id=e1}{-2} ; \htmlData{state=on,id=e4}{2}\right)$.

$\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{D}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{E}}\\ \htmlData{state=on,id=e4}{y_\mathrm{D}}\htmlData{state=hl,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{E}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-2}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-8)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{2}\htmlData{state=hl,id=e5}{-}\htmlData{state=off,id=e6}{6}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=off,id=e9}{6}\\ \htmlData{state=off,id=e8}{-4} \end{pmatrix}$

moins ...

3. $\overrightarrow{\mathrm{ED}}$ avec $\mathrm{E}\left(\htmlData{state=on,id=e3}{-8} ;\htmlData{state=hl,id=e6}{6}\right)$ et $\mathrm{D}\left(\htmlData{state=on,id=e1}{-2} ; \htmlData{state=on,id=e4}{2}\right)$.

$\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{D}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{E}}\\ \htmlData{state=on,id=e4}{y_\mathrm{D}}\htmlData{state=on,id=e5}{-}\htmlData{state=hl,id=e6}{y_\mathrm{E}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-2}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-8)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{2}\htmlData{state=on,id=e5}{-}\htmlData{state=hl,id=e6}{6}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=off,id=e9}{6}\\ \htmlData{state=off,id=e8}{-4} \end{pmatrix}$

Le nombre $y_\mathrm{E}$ est l'ordonnée du point $\mathrm{E}$, c'est $6$.

3. $\overrightarrow{\mathrm{ED}}$ avec $\mathrm{E}\left(\htmlData{state=on,id=e3}{-8} ;\htmlData{state=on,id=e6}{6}\right)$ et $\mathrm{D}\left(\htmlData{state=on,id=e1}{-2} ; \htmlData{state=on,id=e4}{2}\right)$.

$\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{D}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{E}}\\ \htmlData{state=on,id=e4}{y_\mathrm{D}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{E}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-2}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-8)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{2}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{6}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=off,id=e9}{6}\\ \htmlData{state=off,id=e8}{-4} \end{pmatrix}$

On effectue les calculs.

3. $\overrightarrow{\mathrm{ED}}$ avec $\mathrm{E}\left(\htmlData{state=on,id=e3}{-8} ;\htmlData{state=on,id=e6}{6}\right)$ et $\mathrm{D}\left(\htmlData{state=on,id=e1}{-2} ; \htmlData{state=on,id=e4}{2}\right)$.

$\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{D}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{E}}\\ \htmlData{state=on,id=e4}{y_\mathrm{D}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{E}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=hl,id=e9}{\htmlData{state=on,id=e1}{-2}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-8)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{2}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{6}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=hl,id=e9}{6}\\ \htmlData{state=off,id=e8}{-4} \end{pmatrix}$

$-2-\left(-8\right)=-2+8=6$

3. $\overrightarrow{\mathrm{ED}}$ avec $\mathrm{E}\left(\htmlData{state=on,id=e3}{-8} ;\htmlData{state=on,id=e6}{6}\right)$ et $\mathrm{D}\left(\htmlData{state=on,id=e1}{-2} ; \htmlData{state=on,id=e4}{2}\right)$.

$\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{D}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{E}}\\ \htmlData{state=on,id=e4}{y_\mathrm{D}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{E}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-2}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-8)}}\\ \htmlData{state=hl,id=e8}{\htmlData{state=on,id=e4}{2}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{6}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e9}{6}\\ \htmlData{state=hl,id=e8}{-4} \end{pmatrix}$

$2-6=-4$

3. $\overrightarrow{\mathrm{ED}}$ avec $\mathrm{E}\left(\htmlData{state=on,id=e3}{-8} ;\htmlData{state=on,id=e6}{6}\right)$ et $\mathrm{D}\left(\htmlData{state=on,id=e1}{-2} ; \htmlData{state=on,id=e4}{2}\right)$.

$\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{D}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{E}}\\ \htmlData{state=on,id=e4}{y_\mathrm{D}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{E}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-2}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-8)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{2}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{6}} \end{pmatrix}$ $\overrightarrow{\mathrm{ED}}\begin{pmatrix} \htmlData{state=on,id=e9}{6}\\ \htmlData{state=on,id=e8}{-4} \end{pmatrix}$

4. $\overrightarrow{\mathrm{FP}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{-7} ;\htmlData{state=on,id=e6}{-8}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{1} ; \htmlData{state=on,id=e4}{-7}\right)$.

$\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=off,id=e1}{1}\htmlData{state=off,id=e2}{-}\htmlData{state=off,id=e3}{(-7)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{-7}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-8)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=off,id=e9}{8}\\ \htmlData{state=off,id=e8}{1} \end{pmatrix}$

Voici la formule qui permet de calculer les coordonnées de $\overrightarrow{\mathrm{FP}}$

4. $\overrightarrow{\mathrm{FP}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{-7} ;\htmlData{state=on,id=e6}{-8}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{1} ; \htmlData{state=on,id=e4}{-7}\right)$.

$\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=off,id=e1}{1}\htmlData{state=off,id=e2}{-}\htmlData{state=off,id=e3}{(-7)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{-7}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-8)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=off,id=e9}{8}\\ \htmlData{state=off,id=e8}{1} \end{pmatrix}$

Appliquons cette formule.

4. $\overrightarrow{\mathrm{FP}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{-7} ;\htmlData{state=on,id=e6}{-8}\right)$ et $\mathrm{P}\left(\htmlData{state=hl,id=e1}{1} ; \htmlData{state=on,id=e4}{-7}\right)$.

$\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=hl,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=hl,id=e1}{1}\htmlData{state=off,id=e2}{-}\htmlData{state=off,id=e3}{(-7)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{-7}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-8)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=off,id=e9}{8}\\ \htmlData{state=off,id=e8}{1} \end{pmatrix}$

Le nombre $x_\mathrm{P}$ est l'abscisse du point $\mathrm{P}$, c'est $1$.

4. $\overrightarrow{\mathrm{FP}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{-7} ;\htmlData{state=on,id=e6}{-8}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{1} ; \htmlData{state=on,id=e4}{-7}\right)$.

$\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=hl,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{1}\htmlData{state=hl,id=e2}{-}\htmlData{state=off,id=e3}{(-7)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{-7}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-8)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=off,id=e9}{8}\\ \htmlData{state=off,id=e8}{1} \end{pmatrix}$

moins ...

4. $\overrightarrow{\mathrm{FP}}$ avec $\mathrm{F}\left(\htmlData{state=hl,id=e3}{-7} ;\htmlData{state=on,id=e6}{-8}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{1} ; \htmlData{state=on,id=e4}{-7}\right)$.

$\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=hl,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{1}\htmlData{state=on,id=e2}{-}\htmlData{state=hl,id=e3}{(-7)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{-7}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-8)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=off,id=e9}{8}\\ \htmlData{state=off,id=e8}{1} \end{pmatrix}$

Le nombre $x_\mathrm{F}$ est l'abscisse du point $\mathrm{F}$, c'est $-7$.

4. $\overrightarrow{\mathrm{FP}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{-7} ;\htmlData{state=on,id=e6}{-8}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{1} ; \htmlData{state=hl,id=e4}{-7}\right)$.

$\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=hl,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{1}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-7)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=hl,id=e4}{-7}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{(-8)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=off,id=e9}{8}\\ \htmlData{state=off,id=e8}{1} \end{pmatrix}$

Le nombre $y_\mathrm{P}$ est l'ordonnée du point $\mathrm{P}$, c'est $-7$.

4. $\overrightarrow{\mathrm{FP}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{-7} ;\htmlData{state=on,id=e6}{-8}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{1} ; \htmlData{state=on,id=e4}{-7}\right)$.

$\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=hl,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{1}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-7)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{-7}\htmlData{state=hl,id=e5}{-}\htmlData{state=off,id=e6}{(-8)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=off,id=e9}{8}\\ \htmlData{state=off,id=e8}{1} \end{pmatrix}$

moins ...

4. $\overrightarrow{\mathrm{FP}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{-7} ;\htmlData{state=hl,id=e6}{-8}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{1} ; \htmlData{state=on,id=e4}{-7}\right)$.

$\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=hl,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{1}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-7)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{-7}\htmlData{state=on,id=e5}{-}\htmlData{state=hl,id=e6}{(-8)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=off,id=e9}{8}\\ \htmlData{state=off,id=e8}{1} \end{pmatrix}$

Le nombre $y_\mathrm{F}$ est l'ordonnée du point $\mathrm{F}$, c'est $-8$.

4. $\overrightarrow{\mathrm{FP}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{-7} ;\htmlData{state=on,id=e6}{-8}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{1} ; \htmlData{state=on,id=e4}{-7}\right)$.

$\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{1}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-7)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{-7}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{(-8)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=off,id=e9}{8}\\ \htmlData{state=off,id=e8}{1} \end{pmatrix}$

On effectue les calculs.

4. $\overrightarrow{\mathrm{FP}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{-7} ;\htmlData{state=on,id=e6}{-8}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{1} ; \htmlData{state=on,id=e4}{-7}\right)$.

$\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=hl,id=e9}{\htmlData{state=on,id=e1}{1}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-7)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{-7}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{(-8)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=hl,id=e9}{8}\\ \htmlData{state=off,id=e8}{1} \end{pmatrix}$

$1-\left(-7\right)=1+7=8$

4. $\overrightarrow{\mathrm{FP}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{-7} ;\htmlData{state=on,id=e6}{-8}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{1} ; \htmlData{state=on,id=e4}{-7}\right)$.

$\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{1}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-7)}}\\ \htmlData{state=hl,id=e8}{\htmlData{state=on,id=e4}{-7}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{(-8)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e9}{8}\\ \htmlData{state=hl,id=e8}{1} \end{pmatrix}$

$-7-\left(-8\right)=-7+8=1$

4. $\overrightarrow{\mathrm{FP}}$ avec $\mathrm{F}\left(\htmlData{state=on,id=e3}{-7} ;\htmlData{state=on,id=e6}{-8}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{1} ; \htmlData{state=on,id=e4}{-7}\right)$.

$\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{F}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{F}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{1}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-7)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{-7}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{(-8)}} \end{pmatrix}$ $\overrightarrow{\mathrm{FP}}\begin{pmatrix} \htmlData{state=on,id=e9}{8}\\ \htmlData{state=on,id=e8}{1} \end{pmatrix}$

5. $\overrightarrow{\mathrm{CP}}$ avec $\mathrm{C}\left(\htmlData{state=on,id=e3}{-2} ;\htmlData{state=on,id=e6}{5}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{-4} ; \htmlData{state=on,id=e4}{5}\right)$.

$\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{C}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{C}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=off,id=e1}{-4}\htmlData{state=off,id=e2}{-}\htmlData{state=off,id=e3}{(-2)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{5}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{5}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=off,id=e9}{-2}\\ \htmlData{state=off,id=e8}{0} \end{pmatrix}$

Voici la formule qui permet de calculer les coordonnées de $\overrightarrow{\mathrm{CP}}$

5. $\overrightarrow{\mathrm{CP}}$ avec $\mathrm{C}\left(\htmlData{state=on,id=e3}{-2} ;\htmlData{state=on,id=e6}{5}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{-4} ; \htmlData{state=on,id=e4}{5}\right)$.

$\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{C}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{C}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=off,id=e1}{-4}\htmlData{state=off,id=e2}{-}\htmlData{state=off,id=e3}{(-2)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{5}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{5}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=off,id=e9}{-2}\\ \htmlData{state=off,id=e8}{0} \end{pmatrix}$

Appliquons cette formule.

5. $\overrightarrow{\mathrm{CP}}$ avec $\mathrm{C}\left(\htmlData{state=on,id=e3}{-2} ;\htmlData{state=on,id=e6}{5}\right)$ et $\mathrm{P}\left(\htmlData{state=hl,id=e1}{-4} ; \htmlData{state=on,id=e4}{5}\right)$.

$\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=hl,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{C}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{C}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=hl,id=e1}{-4}\htmlData{state=off,id=e2}{-}\htmlData{state=off,id=e3}{(-2)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{5}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{5}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=off,id=e9}{-2}\\ \htmlData{state=off,id=e8}{0} \end{pmatrix}$

Le nombre $x_\mathrm{P}$ est l'abscisse du point $\mathrm{P}$, c'est $-4$.

5. $\overrightarrow{\mathrm{CP}}$ avec $\mathrm{C}\left(\htmlData{state=on,id=e3}{-2} ;\htmlData{state=on,id=e6}{5}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{-4} ; \htmlData{state=on,id=e4}{5}\right)$.

$\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=hl,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{C}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{C}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-4}\htmlData{state=hl,id=e2}{-}\htmlData{state=off,id=e3}{(-2)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{5}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{5}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=off,id=e9}{-2}\\ \htmlData{state=off,id=e8}{0} \end{pmatrix}$

moins ...

5. $\overrightarrow{\mathrm{CP}}$ avec $\mathrm{C}\left(\htmlData{state=hl,id=e3}{-2} ;\htmlData{state=on,id=e6}{5}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{-4} ; \htmlData{state=on,id=e4}{5}\right)$.

$\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=hl,id=e3}{x_\mathrm{C}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{C}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-4}\htmlData{state=on,id=e2}{-}\htmlData{state=hl,id=e3}{(-2)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=off,id=e4}{5}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{5}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=off,id=e9}{-2}\\ \htmlData{state=off,id=e8}{0} \end{pmatrix}$

Le nombre $x_\mathrm{C}$ est l'abscisse du point $\mathrm{C}$, c'est $-2$.

5. $\overrightarrow{\mathrm{CP}}$ avec $\mathrm{C}\left(\htmlData{state=on,id=e3}{-2} ;\htmlData{state=on,id=e6}{5}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{-4} ; \htmlData{state=hl,id=e4}{5}\right)$.

$\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{C}}\\ \htmlData{state=hl,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{C}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-4}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-2)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=hl,id=e4}{5}\htmlData{state=off,id=e5}{-}\htmlData{state=off,id=e6}{5}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=off,id=e9}{-2}\\ \htmlData{state=off,id=e8}{0} \end{pmatrix}$

Le nombre $y_\mathrm{P}$ est l'ordonnée du point $\mathrm{P}$, c'est $5$.

5. $\overrightarrow{\mathrm{CP}}$ avec $\mathrm{C}\left(\htmlData{state=on,id=e3}{-2} ;\htmlData{state=on,id=e6}{5}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{-4} ; \htmlData{state=on,id=e4}{5}\right)$.

$\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{C}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=hl,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{C}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-4}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-2)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{5}\htmlData{state=hl,id=e5}{-}\htmlData{state=off,id=e6}{5}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=off,id=e9}{-2}\\ \htmlData{state=off,id=e8}{0} \end{pmatrix}$

moins ...

5. $\overrightarrow{\mathrm{CP}}$ avec $\mathrm{C}\left(\htmlData{state=on,id=e3}{-2} ;\htmlData{state=hl,id=e6}{5}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{-4} ; \htmlData{state=on,id=e4}{5}\right)$.

$\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{C}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=hl,id=e6}{y_\mathrm{C}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-4}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-2)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{5}\htmlData{state=on,id=e5}{-}\htmlData{state=hl,id=e6}{5}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=off,id=e9}{-2}\\ \htmlData{state=off,id=e8}{0} \end{pmatrix}$

Le nombre $y_\mathrm{C}$ est l'ordonnée du point $\mathrm{C}$, c'est $5$.

5. $\overrightarrow{\mathrm{CP}}$ avec $\mathrm{C}\left(\htmlData{state=on,id=e3}{-2} ;\htmlData{state=on,id=e6}{5}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{-4} ; \htmlData{state=on,id=e4}{5}\right)$.

$\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{C}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{C}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-4}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-2)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{5}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{5}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=off,id=e9}{-2}\\ \htmlData{state=off,id=e8}{0} \end{pmatrix}$

On effectue les calculs.

5. $\overrightarrow{\mathrm{CP}}$ avec $\mathrm{C}\left(\htmlData{state=on,id=e3}{-2} ;\htmlData{state=on,id=e6}{5}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{-4} ; \htmlData{state=on,id=e4}{5}\right)$.

$\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{C}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{C}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=hl,id=e9}{\htmlData{state=on,id=e1}{-4}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-2)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{5}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{5}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=hl,id=e9}{-2}\\ \htmlData{state=off,id=e8}{0} \end{pmatrix}$

$-4-\left(-2\right)=-4+2=-2$

5. $\overrightarrow{\mathrm{CP}}$ avec $\mathrm{C}\left(\htmlData{state=on,id=e3}{-2} ;\htmlData{state=on,id=e6}{5}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{-4} ; \htmlData{state=on,id=e4}{5}\right)$.

$\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{C}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{C}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-4}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-2)}}\\ \htmlData{state=hl,id=e8}{\htmlData{state=on,id=e4}{5}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{5}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e9}{-2}\\ \htmlData{state=hl,id=e8}{0} \end{pmatrix}$

$5-5=0$

5. $\overrightarrow{\mathrm{CP}}$ avec $\mathrm{C}\left(\htmlData{state=on,id=e3}{-2} ;\htmlData{state=on,id=e6}{5}\right)$ et $\mathrm{P}\left(\htmlData{state=on,id=e1}{-4} ; \htmlData{state=on,id=e4}{5}\right)$.

$\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e1}{x_\mathrm{P}}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{x_\mathrm{C}}\\ \htmlData{state=on,id=e4}{y_\mathrm{P}}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{y_\mathrm{C}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e9}{\htmlData{state=on,id=e1}{-4}\htmlData{state=on,id=e2}{-}\htmlData{state=on,id=e3}{(-2)}}\\ \htmlData{state=on,id=e8}{\htmlData{state=on,id=e4}{5}\htmlData{state=on,id=e5}{-}\htmlData{state=on,id=e6}{5}} \end{pmatrix}$ $\overrightarrow{\mathrm{CP}}\begin{pmatrix} \htmlData{state=on,id=e9}{-2}\\ \htmlData{state=on,id=e8}{0} \end{pmatrix}$

Seconde - Calculer les coordonnées d'un vecteur - Episode 2

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