Question

If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

Answer 1

Given: ▱ ABCD is a parallelogram where A (1, 2), B (4, y), C (x, 6) and D (3, 5). 

In a parallelogram, diagonals bisect each other. i.e., the midpoints of the diagonals coincide with each other. 

i.e., midpoint of AC = midpoint of BD

⇒ 1 + x = 7 and 8 = y + 5

⇒ x = 7 – 1 and y = 8 – 5 

∴ x = 6 and y = 3.