If three consecutive vertices of a parallelogram ABCD are A(1, – 2), B(3, 6) and C(5, 10), find its fourth vertex D.

Question

Philoid · Accepted Answer

Coordinate of mid – point of AC = {(1 + 5)/2,(– 2 + 10)/2}

implies (3,4)

This is equal to the coordinates of mid – point of BD

3 = (3 + x)/2

6 = 3 + x

x = 3

4 = (6 + y)/2

8 = (6 + y)

y = 2

Hence, D(3, 2)