Question

On plotting the points $P(0,0),Q(2,0)andR(0,3)$and joining $PQ,QR,PR,$which of the following figure is obtained?

• A.
  Equilateral triangle
• B.
  Isosceles triangle
• C.
  Right-angled triangle
• D.
  Right-angled isosceles triangle

Answer 1

The correct option is C

Right-angled triangle
Given: P(0, 0), Q(2, 0) and R(0, 3)

By distance formula,
$PQ=\sqrt{(2-0{)}^2+(0-0{)}^2}=2unitsPR=\sqrt{(0-0{)}^2+(3-0{)}^2}=3unitsQR=\sqrt{(0-2{)}^2+(3-0{)}^2}=\sqrt{4+9}=\sqrt{13}units$

$\therefore PQ\ne PR\ne QR$

Consider, $P{Q}^2+P{R}^2=2^2+3^2=4+9=13=Q{R}^2\Rightarrow P{Q}^2+P{R}^2=Q{R}^2$

Therefore, $\Delta PQR$ follows Pythagoras theorem.

Thus, $\Delta PQR$ is a right angle triangle, right-angled at $\angle P$.

Hence, the correct answer is option (c).