Question

Three consecutive vertices of a rhombus are (5,3), (2,7) and (-2,4). Find the fourth vertex.

Answer 1

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

We know that diagonals of a rhombus bisect each other.

∴ Midpoint of AC = Midpoint of BD …(i)

Coordinates of the midpoint of AC are

⇒ 2 + x = 3 and 7 + y = 7

⇒ x = 1 and y = 0

Thus, the coordinates of the vertex D are (1, 0)