Prove, using co -

Let us assume ABCD be a rectangle with A as the origin and AB and AD as x and y - axes having lengths a and b units.

We get the vertices of the rectangle as follows.

⇒ A = (0, 0)

⇒ B = (a, 0)

⇒ C = (a, b)

⇒ D = (0, b)

We need to prove the lengths of the diagonals are equal.

i.e., AC = BD

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

Let us find the individual lengths of diagonals,

⇒

⇒ ..... (1)

⇒

⇒ ..... (2)

From (1) and (2), we can clearly say that AC = BD.

∴ The diagonals of a rectangle are equal.