Réponse :
Bonjour,
Explications étape par étape
[tex]\overrightarrow{U}=4*\vec{i}+5*\vec{j}\\\\\overrightarrow{V}=8*\vec{i}-5*\vec{j}\\\\\\A=(-6,-3)\\B=(x_B,y_B)\\C=(x_C,y_C)\\\\\overrightarrow{AB}=(x_B+6)*\vec{i}+(y_B+3)*\vec{j}\\\\\\\overrightarrow{AB}=\overrightarrow{U}\\\\(x_B+6)*\vec{i}+(y_B+3)*\vec{j}=4*\vec{i}+5*\vec{j}\\\\\left\{\begin{array}{ccc}x_B+6&=&4\\y_B+3&=&5\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x_B&=&-2\\y_B&=&2\\\end{array}\right.\\[/tex]
[tex]\overrightarrow{BC}=(x_C+x_B)*\vec{i}+(y_C+y_B)*\vec{j}\\=(x_C+2)*\vec{i}+(y_C-2)*\vec{j}=8*\vec{i}-5*\vec{j}\\\\\left\{\begin{array}{ccc}x_C+2&=&8\\y_C-2&=&-5\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x_C&=&6\\y_C&=&-3\\\end{array}\right.\\[/tex]
b)
B'= mil[AB]=((-6+(-2))/2,(-3+2)/2)=(-4,-1/2
C'=(0,-3)
c)
[tex]\overrightarrow{BC}=2*\overrightarrow{B'C'}\\[/tex]
