Question

A(–1, 0), B(1, 3) and D(3, 5) are the vertices of a parallelogram ABCD. Find the co-ordinates of vertex C.

Answer 1

Let the co-ordinates of vertex C be (x, y).

ABCD is a parallelogram.

∴ Mid-point of AC = Mid-point of BD

`((-1 + x)/2, (0 + y)/2) = ((1 + 3)/2, (3 + 5)/2)`

`((-1 + x)/2, y/2) = (2,4)`

`(-1 + x)/2 = 2 and y/2 = 4`

`x = 5` and `y/2 = 4`

x = 5 and y = 8

Thus, the co-ordinates of vertex C is (5, 8).