Let $P=(-1,0), Q=(0,0)$ and $R=(3,3 \sqrt{3})$ be three points. Then the equation of the bisector of the $\angle \mathrm{PQR}$ is

• Correct answer
  A

  $\sqrt{3 x}+y=0$
• B

  $x+\frac{\sqrt{3}}{2} y=0$
• C

  $\frac{-\sqrt{3}}{2} x+y=0$
• D

  $x+\sqrt{3} y=0$

Solution

Given $\mathrm{P}(-1,0), \mathrm{B}=(0,0), R=(3,3 \sqrt{3})$
Now slope of line $Q M=\tan \frac{2 \pi}{3}=-\sqrt{3}$ $\therefore$ Equation of line $Q M=y-\sqrt{3} x=0 \Rightarrow \sqrt{3} x+y=0$

Hence, the correct answer is option: 'A'.