The three vertices of a parallelogram ABCD, taken in order are A (1, – 2), B (3, 6) and C (5, 10). Find the coordinates of the fourth vertex D.

Question

Philoid · Accepted Answer

Let the coordinates of the fourth vertex D be (x₄,y₄).

We know that –

Diagonals of a ∥gm bisect each other.

∴ Mid – point of diagonal AC ≡ Mid – point of diagonal BD

⇒ 6 = 3 + x₄ and 8 = 6 + y₄

⇒ x₄ = 3 and y₄ = 2

Thus, the coordinates of the fourth vertex D is (3,2).