Q28 of 184 Page 10

Prove, using co - ordinates that diagonals of a rectangle are equal.

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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