Question

On plotting of point $P(0,a),Q(0,–a),R(b,0)\text{and}S(–b,0)$, where $a,b$ are distinct real numbers. $PRQS$ is not always a/an

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

Answer 1

The correct option is D

Square
By distance formula,



$PR=\sqrt{(b-0{)}^2+(0-a{)}^2}=\sqrt{a^2+b^2}QR=\sqrt{(b-0{)}^2+(0+a{)}^2}=\sqrt{a^2+b^2}$

Similarly, $PS=SQ=\sqrt{a^2+b^2}$ and, $PQ=\sqrt{(0-0{)}^2+(-a-a{)}^2}=2a$
also, $RS=\sqrt{(-b-b{)}^2+(0+0{)}^2}=2b$

Now, $a$ and $b$ are distinct real numbers.

$\therefore PQ\ne RS$

Thus, PRQS cannot be a square.

Hence, the correct answer is option (d).