Question

Prove that the points (4, 5), (7, 6), (6, 3), (3, 2) are the vertices of a parallelogram. Is it a rectangle.

Answer 1

Let A(4, 5), B(7, 6), C(6, 3), and D(3, 2) be the given points.

And, P the points of intersection of AC and BD.

Coordinates of the mid-point of AC are

Coordinates of the mid-point of BD are 

Thus, AC and BD have the same mid-point.

Hence, ABCD is a parallelogram

Now, we shall see whether ABCD is a rectangle.

We have,

So, ABCD is not a rectangle.