Question

The quadrilateral formed by the points $P(-5,0),Q(-3,-1),R(-2,5)$ and $S(-4,6)$ is a

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

Answer 1

The correct option is C Parallelogram

$P(-5,0),Q(-3,-1),R(-2,5)$ and $S(-4,6)$
Now, finding the distance
$PQ=\sqrt{(-5+3{)}^2+(0+1{)}^2}=\sqrt{5}\text{units}QR=\sqrt{(-3+2{)}^2+(-1-5{)}^2}=\sqrt{37}\text{units}RS=\sqrt{(-2+4{)}^2+(5-6{)}^2}=\sqrt{5}\text{units}SP=\sqrt{(-4+5{)}^2+(6-0{)}^2}=\sqrt{37}\text{units}$
So, opposite sides are equal in length, now finding the diagonal lengths,
$PR=\sqrt{(-5+2{)}^2+(0-5{)}^2}=\sqrt{34}\text{units}QS=\sqrt{(-3+4{)}^2+(-1-6{)}^2}=\sqrt{50}\text{units}$
As the diagonals are unequal so it is a parallelogram.