Find the coordinates of D in the parallelogram

Question

Given parallelogram ABCD with A (2,10), B(4,6) and C(1,1). Give the coordinates of vertex D.

Answer 1

AB = CD or CD = - AB, AB and CD are vectors; So if D(x, y), then CD = <x - 1, y - 1>; AB = <1 - 2, 6 - 10> =

< -1, - 4>.;

CD = AB: <x - 1, y - 1> = <- 1, - 4>; x - 1 = - 1; x = 0; y - 1 = - 4; y = - 3; D(0, -3)

CD = - AB: <x - 1, y - 1> = <1, 4>; x - 1 = 1; x = 2; y - 1 = 4; y = 5; D(2, 5) : ,