Question

Show that the points A(1, 0), B(5, 3), C(2, 7) and D(- 2, 4) are the vertices of a rhombus.

Answer 1

Given points are A(1, 0), B(5, 3), C(2, 7) and D(- 2, 4).

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

We know that in the lengths of sides are equal in a rhombus and the length of diagonals are not equal.

Let us find the lengths of the sides.

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

Now,

⇒ BC = 5

⇒ DA = 5

We got AB = BC = CD = DA, these are the vertices of a square or a rhombus.

Now we find the lengths of the diagonals.

We got AC = BD.

∴ The points form a square not rhombus.