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.
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