Question

Prove that the points (-2,-1), (1,0),(4,3) and (1,2) are the vertices of a parallelogram.

Answer 1

Note that to show that a quadrilateral is a parallelogram, it is sufficient to show that the diagonals of the quadrilateral bisect each other.

Let A(-2, -1), B(1, 0), C(4, 3) and D(1, 2) are the vertices of a parallelogram.

Let M be the midpoint of AC, then the coordinates of M are given by

Thus, AC and BD have the same midpoint.

In other words, AC and BD bisect each other.

Hence, ABCD is a parallelogram.