Question

Examine whether the following points taken in order form a square.

(3, 2), (0, 5), (-3, 2) and (0, -1)

Answer 1

Let us consider the given points as $A(3,2);B(0,5);C(-3,2);D(0,-1)$.

The distance between $AB=\sqrt{(3-0{)}^2+(2-5{)}^2}=\sqrt{9+9}=\sqrt{18}$

The distance between $BC=\sqrt{(0+3{)}^2+(5-2{)}^2}=\sqrt{9+9}=\sqrt{18}$

The distance between $CD=\sqrt{(-3-0{)}^2+(2+1{)}^2}=\sqrt{9+9}=\sqrt{18}$

The distance between $DA=\sqrt{(0-3{)}^2+(-1-2{)}^2}=\sqrt{9+9}=\sqrt{18}$

The distance between $AC=\sqrt{(3+3{)}^2+(2-2{)}^2}=\sqrt{36}=6$

The distance between $BD=\sqrt{(0-0{)}^2+(5+1{)}^2}=\sqrt{36}=6$

As the sides are equal $AB=BC=CD=DA$

The diagonals are also equal $AC=BD$.

Therefore, the given points represents square.

Hence, this is the answer.