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

Coordinates of the mid-point of AC are

Coordinates of the mid-point of BD are

AC and BD have the same mid-point

Therefore, ABCDis a parallelogram

Now,

So, ABCD is a parallelogram whose adjacent sides are equal

Therefore, ABCD is a rhombus

We have,

Hence, ABCD is a square.