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Examine whether the following points taken in order form a square. (0, - 1), (2, 1), (0, 3) and ( - 2, 1)

Answers (1)

Let the given points be A(0, - 1), B(2, 1), C(0, 3) and D( - 2, 1) respecievely.

The distances 

\\AB=\sqrt{(2-0)^2+(1-(-1))^2}=\sqrt{8}\\BC=\sqrt{(0-2)^2+(3-1)^2}=\sqrt{8}\\CD=\sqrt{(-2-0)^2+(1-3)^2}=\sqrt{8}\\AD=\sqrt{(-2-0)^2+(1-(-1))^2}=\sqrt{8}\\AC=\sqrt{(0-0)^2+(3-(-1))^2}=\sqrt{16}=4\\BD=\sqrt{(-2-2)^2+(1-1)^2}=\sqrt{16}=4

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

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