Geometry (C10)

If coordinates of two adjacent vertices of a parallelogram are (3, 2), (1, 0) and diagonals bisect each other at (2, –5), find coordinates of the other two vertices.

Answer

Let the coordinates of C and D be (a, b) and (c, d)

∴ (3 + a)/2 = 2

⇒ a = 1

and (2 + b)/2 = –5

⇒ b = –12

Also

(c + 1)/2 = –5

⇒ c = 3

and (d + 0)/2 = –5

⇒ d = –10

∴ Coordinate of C and D are (1, –12) and (3, –10)