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
So, ABCD is a parallelogram whose adjacent sides are equal
Therefore, ABCD is a rhombus
Hence, ABCD is a square.