Bonsoir, j'ai vraiment besoin d'aide pour ces deux exercices. merci d'avance

69 ) A=(3; 5) , B = (-1; 4) et C = (0; 2) 

AD = 3AB.  Soit D=(x; y)
AD= (x-3 ; y-5)
3AB = 3 (-1-3; 4 - 5) = 3 (-4 ; -1) = (-12; -3)
==> x-3 = -12 <==> x = -9
==> y-5 = -3   <==> y = 2
====> D = (-9; 2)

AE = (1/3)AC + 2BC.  Soit E=(x; y)

AE= (x - 3; y - 5)
(1/3)AC + 2BC = (1/3)(-3 ; -3) + 2(1 ; -2) = (-1 ; -1) + (2; -4) = (1; -5)
==> x-3=1 <==> x=4
==> y-5=-5 <==> y=0
====> E=(4; 0)

70) A=(2; -4) , B=(-1; -3) et C = (-1; 2)

OE = -OB <==> E = -B = (1; 3)

AD =(4/3)AC 
AD= (x - 2 ; y +4)
(4/3)AC = (4/3) (-3; 6) = (-4 ; 8)
==> x-2 = -4 <==> x = -2
==> y+4=8 <==> y=4
====> D = (-2; 4)

DF = DE + 2DO 
<==> (x +2; y-4) = (1+2 ; 3-4) + 2(2; -4)
<==> (x+2 ; y-4) = (3; -1) + (4; -8) = (7; -9)
==> x+2 = 7 <==> x=5
==> y-4 = -9 <==> y=-5
===> F=(5; -5)

BA et AF

BA = (3; -1) et AF=(3; -1)

===A est milieu de BF