Prove that the points (-4, -1), (-2, -4), (4, 0) and (2, 3) are the vertices of a rectangle.

Let the given points be A(-4, -1), B(-2, -4), C(4, 0) and D(2, 3).

By distance formula,

XY =

For AB,

AB =

=

=

= units

For BC,

BC =

=

= units

For CD,

CD =

=

= units

For AD,

AD =

=

= units

Also, for diagonal AC,

AC =

=

= units

For diagonal BD,

BD =

=

= units

We can observe that AB = CD and BC = AD and also diagonal AC = BD.

We know that a quadrilateral whose opposite sides are equal and the diagonal are equal is rectangle.

∴ □ABCD is a rectangle.