Question

The quadrilateral formed by the points $(-1,-2),(1,0),(-1,2)$ and $(-3,0)$ is a:

• A. rectangle
• B. square
• C. rhombus
• D. none of these

Answer 1

The correct option is B square

Let $A(-1,-2),B(1,0),C(-1,2)$ and $D(3,0)$.
Distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ can be calculated using the formula $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$
Distance between the points A$(-1,-2)$ and B $(1,0)=\sqrt{{(1+1)}^2+{(0+2)}^2}=\sqrt{4+4}=\sqrt{8}$

Distance between the points B$(1,0)$ and C $(-1,2)=\sqrt{{(-1-1)}^2+{(2-0)}^2}=\sqrt{4+4}=\sqrt{8}$

Distance between the points C$(-1,2)$ and D $(-3,0)=\sqrt{{(-3+1)}^2+{(0-2)}^2}=\sqrt{4+4}=\sqrt{8}$

Distance between the points A$(-1,-2)$ and D $(-3,0)=\sqrt{{(-3+1)}^2+{(0+2)}^2}=\sqrt{4+4}=\sqrt{8}$

Since, length of the sides between all vertices are equal, they are the vertices of a square.