Prove that the diagonals of a rectangle bisect each other and are equal. (Hint:With O as origin, let the vertices of the rectangle be (0, 0), (a, 0), (a, b)and (0, b)).

PROOF:

ABCO is a rectangle with vertices A(a, 0), B(a, b), C(0, b) and O(0, 0).
The midpoint of AC is
The midpoint of OB is

Hence the diagonals bisect each other.
The length of the diagonal AC

The length of the diagonal OB

Hence the diagonals are equal.