Straight Line and Pair of Straight Lines 2 Question 3
3. Let $P=(-1,0)$, and $Q(0,0)$ and $R=(3,3 \sqrt{3})$ be three point. Then, the equation of the bisector of the angle $P Q R$ is
$(2001,1 M)$
(a) $\frac{\sqrt{3}}{2} x+y=0$
(b) $x+\sqrt{3} y=0$
(c) $\sqrt{3} x+y=0$
(d) $x+\frac{\sqrt{3}}{2} y=0$
Assertion and Reason
For the following questions choose the correct answer from the codes (a), (b), (c) and (d) defined as follows.
(a) Statement I is true, Statement II is also true; Statement II is the correct explanation of Statement I
(b) Statement I is true, Statement II is also true; Statement II is not the correct explanation of Statement I (c) Statement I is true; Statement II is false
(d) Statement I is false; Statement II is true
Show Answer
Answer:
Correct Answer: 3. (c)
Solution:
- The line segment $Q R$ makes an angle of $60^{\circ}$ with the positive direction of $X$-axis.
So, the bisector of the angle $P Q R$ will make an angle of $60^{\circ}$ with the negative direction of $X$-axis it will therefore have angle of inclination of $120^{\circ}$ and so, its equation is
$$ \begin{array}{rlrl} & & y-0 & =\tan 120^{\circ}(x-0) \\ \Rightarrow & y & =-\sqrt{3} x \\ \Rightarrow & & y+\sqrt{3} x & =0 \end{array} $$
