Prove that the points A (0, -1), B (-2, 3), C (6, 7) and D (8, 3) are the vertices of a rectangle ABCD?(CBSE 2013)

Length of Side AB is given by-

= 2√5 units

Length of Side BC is given by-

=√(64+16)

=√80

= 4√5 units

Length of Side CD is given by-

=√(4+16)

=√20

= 2√5 units

Length of Side DA is given by-

=√(64+16)

=√80

= 4√5 units

Also,

Length of Diagonal AC is given by-

=√(36+64)

=√100

= 10 units

Length of Diagonal BD is given by-

=√100

= 10 units

Clearly,

Opposite sides AB = CD = 2√5 units

Opposite sides BC = AD = 4√5 units

Diag. AC = BD = 10 units

Thus, Opposite sides are equal and diagonals are also equal.

Hence, ABCD is a rectangle