Question

The three vertices of a parallelogram are (3, 4), (3, 8) and (9, 8). Find the fourth vertex.

Answer 1

Consider A(3, 4), B (3, 8) and C(9, 8).

Let D (x, y) be the fourth vertex of the parallelogram ABCD.

Midpoint of AC = = (6,6)

Midpoint of BD =

Since, the diagonals of parallelogram bisect each other at O.

∴ Mid point of BD = Mid point of AC

= (6,6)

x + 3 = 12 and y + 8 = 12

x = 9 and y = 4
∴ (9, 4) is the fourth vertex.