Question

Find the possible pairs of coordinates of the fourth vertex D of the parallelogram, if three of its vertice are A(5,6),B(1,-2) and C(3,-2).

Answer 1

Let D be (x,y)

Midpoint of AC =  Mid point of BD

MP of AC = (4,2)
MP of BD = (1+x)/2 , (y-2)/2

1+x = 8 ⇒  x = 7
y-2 = 4 ⇒ y = 6

So, D (7,6)