Show that the points A ( - 4, - 1), B ( - 2, - 4), C (4, 0) and D (2, 3) are the vertices points of a rectangle.

Given: A ( - 4, - 1), B ( - 2, - 4), C (4, 0) and D (2, 3)

To prove: The points are vertices of a rectangle.

Formula Used:

The distance between the points (x₁, y₁) and (x₂, y₂) is:

Distance d

Explanation:

Vertices of rectangle ABCD are:

A ( - 4, - 1), B ( - 2, - 4), C (4, 0) and D (2, 3)

By applying the distance formula, we get,

Length of side AB = units

Length of side BC = units

Length of side CD = units

Length of side DA = units

AB = CD

BC = DA

Length of diagonal BD = units

Length of diagonal AC = units

AC = BD

Since opposite sides are equal and diagonal are equal. Therefore, given vertices are the vertices of a rectangle.