# Prove that (4, 3), (6, 4), (5, 6) and (3, 5) are the angular points of a square.

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Prove that (4, 3), (6, 4), (5, 6) and (3, 5) are the angular points of a square.

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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.