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  • Examine whether the following points taken in order to form a square. (3, 2), (0, 5), ( - 3, 2) and (0, - 1)

Examine whether the following points taken in order to form a square. (3, 2), (0, 5), ( - 3, 2) and (0, - 1)

Answers (1)

Let the given points be A(3, 2), B(0, 5), C( - 3, 2) and D(0, - 1)  

The distances 

\\AB=\sqrt{(0-3)^2+(5-2)^2}=\sqrt{18}units\\BC=\sqrt{(-3-0)^2+(2-5)^2}=\sqrt{18}units\\CD=\sqrt{(0-(-3))^2+(-1-2)^2}=\sqrt{18}units\\AD=\sqrt{(0-3)^2+(-1-2)^2}=\sqrt{18}units\\AC=\sqrt{(-3-3)^2+(2-2)^2}=\sqrt{(-6)^2}=6units\\BD=\sqrt{(0-0)^2+(-1-5)^2}=\sqrt{(-6)^2}=6units

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

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Safeer PP

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