Question

Given: The coordinates of rhombus WXYZ are W(0, 4b), X(2a, 0), Y(0, -4b), and Z(-2a, 0).
Prove: The segments joining the midpoints of a rhombus form a rectangle.

Answer 1

In geometry, drawing a diagram to illustrate the given information is half the solution:


First verify that the figure WXYZ is a rhombus (else it might be a wild goose chase).
Since all sides are of length \(L=\sqrt{(2a)^2+(4b)^2}\), yes, WXYZ is a rhombus.

Hints:
Choose one of the following to proceed.
1. A rectangle is a quadrilateral with
- opposite sides parallel and
- diagonals equal.
or
2. A rectangle is a quadrilateral with
- opposite sides parallel with
- at least two pairs of adjacent sides are perpendicular to each other