Question

Prove that the diagonals of a rectangle with vertices (0, 0), (a, 0), (a, b) and (0,b) bisect each other and are equal.

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Answer 1

Step-by-step explanation:

AC and OB are diagonals

In the figure let the intersecting point of OB and AC be P

To show that diagonals bisect each other we have to prove that OP = PB

and PA = PC

The co-ordinates of P is obtained by

half up pic see

OP = OB

Similarly we can prove that PC = PA

Thus diagonals bisect each other in a rectangle .

half down pic see

∴ The diagonals of a rectangle bisects each other and equal .

ok

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