Question

Name the type of the quadrilateral formed by joining the points $A(-1,-2),B(1,0),C(-1,2)$ and $D(-3,0)$ on a graph paper. Justify your answer.

Answer 1

$A=(-1,-2),B=(1,0),C=(-1,2),D=(-3,0)$

By distance formula,

$d(A,B)=\sqrt{(1+1{)}^2+(0+2{)}^2}=2\sqrt{2}$

$d(B,C)=\sqrt{(-1-1{)}^2+(2-0{)}^2}=2\sqrt{2}$

Also, $CD=2\sqrt{2},DA=2\sqrt{2}$

$\therefore AB=BC=CD=AD$ ....(1)

Slope of $AB=\frac{-2}{-2}=1$

Slope of $BC=\frac{2}{-1-1}=-1$

Hence, slope of AB $\times$ slope of BC $=-1$

$\therefore AB$ is perpendicular to $BC$

The lengths of the adjacent sides are equal and they perpendicular to each other.

Therefore, the polygon is a square.