# Examine whether the following points taken in order form a square. (5, 2), (1, 5), ( - 2, 1) and (2, - 2)

Let the given points be A(5, 2), B(1, 5), C( - 2, 1) and D(2, - 2)

The distances

$\\AB=\sqrt{(1-5)^2+(5-2)^2}=5\\BC=\sqrt{(-2-1)^2+(1-5)^2}=5\\CD=\sqrt{(2-(-2))^2+(-2-1)^2}=5\\AD=\sqrt{(2-5)^2+(-2-2)^2}=5\\AC=\sqrt{(-2-5)^2+(1-2)^2}=\sqrt{50}\\BD=\sqrt{(2-1)^2+(-2-5)^2}=\sqrt{50}$

The sides AB=BC=CD=AD and the diagonals AC=BD. Therefore the given points form a square.

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