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.