Question

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

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

Answer 1

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

Given three points $p(-1,0)Q(0,0)R(3,3\sqrt{3})$

Slope of the line $QM$ is Ref. image

$\tan \frac{2\pi }{3}=-\sqrt{3}$

$\therefore$ Equation is line $QM$ which is $y=-\sqrt{3}x$

$\therefore y=-\sqrt{3}x\Rightarrow \sqrt{3}x+y=0$