Prove that the points (4, 8), (0, 2), (3, 0) and (7, 6) are the vertices of a rectangle.

Given points are A(4, 8), B(0, 2), C(3, 0) and D(7, 6).

We need to prove that these are the vertices of a rectangle.

We know that in the lengths of opposite sides and lengths of diagonals are equal in a rectangle.

Let us find the lengths of the sides.

We know that the distance between the points (x₁, y₁) and (x₂, y₂) is .

Now,

⇒ AB = √52

⇒ BC = √13

⇒ CD = √52

⇒ DA = √13

We got AB = CD and BC = DA, these are the vertices of a parallelogram or a rectangle.

Now we find the lengths of the diagonals.

We got AC = BD.

∴ The points form a rectangle.