MHB Finding the Coordinates of Point D

[Ecdownes]

Points A ,B and C have coordinates A(1,3) B(5,1) and C(2,-8).
point D is such that the vector AD = Vector BC + (2x) vector AB + (3y) vectorAC = vector AB + (2x) vectorAC + (3y) vector BC
find coordinates of D

 

[skeeter]

AB = (4,-2), BC = (-3,-9), AC = (1,-11)

let D = (m,n) $\implies$ AD = (m-1,n-3)

AD = (-3,-9) + 2x(4,-2) + 3y(1,-11) = (4,-2) + 2x(1,-11) + 3y(-3,-9)

AD = (-3+8x+3y , -9-4x-33y) = (4+2x-9y , -2-22x-27y)

-3+8x+3y = 4+2x-9y
-9-4x-33y = -2-22x-27y

solve the system for x and y, then determine the coordinates of D