Question

The quadrilateral formed by the points $A(5,-1),B(11,-3),C(5,-5)$ and $D(-1,-3)$ is a

• A. Rhombus
• B. Rectangle
• C. Square
• D. Trapezium

Answer 1

The correct option is A Rhombus

$A(5,-1),B(11,-3),C(5,-5)$ and $D(-1,-3)$
Now, finding the distance
$AB=\sqrt{(5-11{)}^2+(-1+3{)}^2}=\sqrt{40}\text{units}BC=\sqrt{(11-5{)}^2+(-3+5{)}^2}=\sqrt{40}\text{units}CD=\sqrt{(5+1{)}^2+(-5+3{)}^2}=\sqrt{40}\text{units}AD=\sqrt{(5+1{)}^2+(-1+3{)}^2}=\sqrt{40}\text{units}$
All sides are equal so it is a rhombus or square, so calculating the length of the diagonal,
$AC=\sqrt{(5-5{)}^2+(-1+5{)}^2}=4\text{units}BD=\sqrt{(11+1{)}^2+(-3+3{)}^2}=12\text{units}$
As the diagonal is not equal so it is a rhombus.