Question

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

• A. $\frac{\sqrt{3}}{2}x+y=0$
• B. $x+\sqrt{3}y=0$
• C. $\sqrt{3}x+y=0$
• D. $x+\frac{\sqrt{3}}{2}y=0$

Answer 1

The correct option is C $\sqrt{3}x+y=0$

The line segment $QR$ makes an angle ${60}^0$ with the positive direction of x-axis.
So, the bisector of the $\angle PQR$ will make an angle of ${60}^0$ with the negative direction of x-axis.

It will therefore have angle of inclination of ${120}^0$ and so its equation is
$y-0=\tan {120}^0(x-0)$
$\Rightarrow y=-\sqrt{3}x$
$\Rightarrow \sqrt{3}x+y=0$