Question

The points $P(4,3),Q(6,4),R(5,6)$ and $S(3,5)$ respectively are the vertices of a quadrilateral which is

• A. a Square
• B. a Trapezium
• C. a Parallelogram
• D. a Rhombus

Answer 1

The correct option is A a Square

$PQ=\sqrt{(4-6{)}^2+(3-4{)}^2}=\sqrt{5}\text{units}$
$QR=\sqrt{(6-5{)}^2+(4-6{)}^2}=\sqrt{5}\text{units}$
$RS=\sqrt{(5-3{)}^2+(6-5{)}^2}=\sqrt{5}\text{units}$
$PS=\sqrt{(4-3{)}^2+(3-5{)}^2}=\sqrt{5}\text{units}$

$PR=\sqrt{(4-5{)}^2+(3-6{)}^2}=\sqrt{10}\text{units}QS=\sqrt{(6-3{)}^2+(4-5{)}^2}=\sqrt{10}\text{units}$
So,
$PQ=QR=RS=SP$
And
$PR=QS$

Hence, it is a square.