Question

A (−2, 3) and B (3, −1) are two vertices of a paralļelogram ABCD. Its diagonals interested each other at point (1, 5), find the co-ordinates of C and D.

Answer 1

The diagonals of a parallelogram bisect each other, so the given intersection M (1, 5) is the midpoint of AC and of BD.

Here, let,

• A = (−2, 3),
• B = (3, −1),
• M = (1, 5)

Then,

⇒ C = 2M − A

= (2 × 1 − (−2), 2 × 5 − 3)

= (2 + 2, 10 − 3)

∴ C = (4, 7)

⇒ D = 2M − B

= (2 × 1 − 3, 2 × 5 − (−1))

= (2 − 3, 10 + 1)

∴ D = (−1, 11)

Hence, C = (4, 7) and D = (−1, 11).