Question

The area of rectangles whose vertices are $(0,-1),(6,7),(-2,3)$ and $(8,3)$ is

• A. $10\sqrt{5}$ sq. units
• B. $\sqrt{5}$ sq. units
• C. $40$ sq. units
• D. $40\sqrt{5}$ sq. units

Answer 1

The correct option is D $40\sqrt{5}$ sq. units

Let the rectangle be $ABCD$ with $A=(x_1,y_1)=(0,-1),B=(x_2,y_2)=(6,7),C=(x_3,y_3)=(-2,3)$ and $D=(x_4,y_4)=(8,3)$

$\therefore AB=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}=\sqrt{{(6-0)}^2+{(7+1)}^2}=10$ units and

$\therefore BC=\sqrt{{(x_3-x_2)}^2+{(y_3-y_2)}^2}=\sqrt{{(-2-6)}^2+{(3-7)}^2}=4\sqrt{5}$ units

$\therefore ar\left(ABCD\right)=AB\times BC=10\times 4\sqrt{5}=40\sqrt{5}$ sq. units.

Therefore, area of rectangle is $40\sqrt{5}$ sq. units.