Given: Vertices of the quadrilateral are A(1, -2), B(3, 6), C(5, 10) and D(3, 2).

Note: For a quadrilateral to be a parallelogram opposite sides of the quadrilateral must be equal in length, and the diagonals must not be equal.

AB

= 2√17 units

BC

= 2√5 units

CD

= 2√17 units

DA

= 2√5 units

Therefore, AB = CD and BC = DA …..(1)

AC

= 4√10 units

BD

= 4 units

Therefore, AC BD …..(2)

From 1 and 2, we have

Opposite sides of ABCD are equal, and diagonals are not equal. Hence, points A, B, C and D are the vertices of a parallelogram.