Let P=(-1,0), Q=(0,0) and R=(3,3√3) be three points.

Question

Let $P=(-1,0),\ Q=(0,0)$ and $R=(3,3\sqrt3)$ be three points. The equation of the bisector of the angle $PQR$ is:

Accepted Answer

Given : The coordinates of points $P,Q,R$ are $(-1,0),$

$$\left( {0,0} \right),\,\left( {3,3\sqrt 3 } \right)$$ respectively

Slope of $QR$ $$ = {{{y_2} - {y_1}} \over {{x_2} - {x_1}}} = {{3\sqrt 3 } \over 3}$$

$$ \Rightarrow \tan \theta  = \sqrt 3  \Rightarrow \theta  = {\pi  \over 3}$$

$$ \Rightarrow \angle RQX = {\pi  \over 3}$$

$$\therefore$$ $$\angle RQP = \pi  - {\pi  \over 3} = {{2\pi } \over 3}$$

Let $QM$ bisects the $$\angle PQR,$$

$$\therefore$$ Slope of the line $QM=tan$ $${{2\pi } \over 3} =  - \sqrt 3 $$

$$\therefore$$ Equation of line $QM$ is $$\left( {y - 0} \right) =  - \sqrt 3 \left( {x - 0} \right)$$

$$ \Rightarrow y =  - \sqrt 3 \,x \Rightarrow \sqrt 3 x + y = 0$$

Solutions · 1