Question

Show that the quadrilateral whose vertices are (2, −1), (3, 4) (−2, 3) and (−3,−2) is a rhombus.

Answer 1

The distance d between two points and is given by the formula

In a rhombus all the sides are equal in length.

Here the four points are A (2, −1), B (3, 4), C (−2, 3) and D (−3, −2).

First let us check if all the four sides are equal.

Here, we see that all the sides are equal, so it has to be a rhombus.