Prove that the diagonals of a rectangle ABCD with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6) are equal and bisect each other.

Question

Philoid · Accepted Answer

fig.3

Length of diagonal AC is given by-

√(9 + 49)

= √58 units

Length of diagonal BD is given by-

= √(9 + 49)

= √58 units

Clearly, the length of the diagonals of the rectangle ABCD are equal.

Mid-point of Diagonal AC is given by

Similarly, Mid-point of Diagonal BD is given by

Clearly, the coordinates of mid-point of both the diagonals coincide i.e. diagonals of the rectangle bisect each other.