Question

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

(-1, 2), (1, 0), (3, 2) and (1, 4)

Answer 1

Let us consider the given points as $A(-1,2);B(1,0);C(3,2);D(1,4)$.

The distance between $AB=\sqrt{(-1-1{)}^2+(2-0{)}^2}=\sqrt{4+4}=\sqrt{8}$

The distance between $BC=\sqrt{(1-3{)}^2+(0-2{)}^2}=\sqrt{4+4}=\sqrt{8}$

The distance between $CD=\sqrt{(3-1{)}^2+(2-4{)}^2}=\sqrt{4+4}=\sqrt{8}$

The distance between $DA=\sqrt{(1+1{)}^2+(4-2{)}^2}=\sqrt{4+4}=\sqrt{8}$

The distance between $AC=\sqrt{(-1-3{)}^2+(2-2{)}^2}=\sqrt{16}=4$

The distance between $BD=\sqrt{(1-1{)}^2+(0-4{)}^2}=\sqrt{16}=4$

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.