Question

In the graph, P and Q are two vertices of quadrilateral PQRS.
Given that coordinates of R and S are $(4,2)$ and $(1,-1)$ respectively, the quadrilateral
PQRS is a

• A. rectangle
• B. square
• C. rhombus
• D. trapezium

Answer 1

The correct option is B square

$P\equiv (-2,2);Q\equiv (1,5);R\equiv (4,2);S\equiv (1,-1)$

$PQ=\sqrt{{(1+2)}^2+{(5-2)}^2}=3\sqrt{2}QR=\sqrt{{(4-1)}^2+{(5-2)}^2}=3\sqrt{2}RS=\sqrt{{(4-1)}^2+{(-1-2)}^2}=3\sqrt{2}PS=\sqrt{{(1+2)}^2+{(2+1)}^2}=3\sqrt{2}PR=\sqrt{{(4+2)}^2+{(2-2)}^2}=6QS=\sqrt{{(1-1)}^2+{(5-(-1\left)\right)}^2}=6$

Since, all sides $PQ,QR,RS$ and $PS$ are equal,

also, diagonals $PR$ and $QS$ are also equal to each other,

We can say say that $PQRS$ is a square.