Straight Line and Pair of Straight Lines 2 Question 1
1. A ray of light along $x+\sqrt{3} y=\sqrt{3}$ gets reflected upon reaching $X$-axis, the equation of the reflected ray is
(a) $y=x+\sqrt{3}$
(b) $\sqrt{3} y=x-\sqrt{3}$
(c) $y=\sqrt{3 x}-\sqrt{3}$
(d) $\sqrt{3} y=x-1$
(2013 Main)
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Answer:
Correct Answer: 1. (b)
Solution:
- Take any point $B(0,1)$ on given line.
Equation of $A B$ is
$$ \begin{aligned} & y-0=\frac{-1-0}{0-\sqrt{3}}(x-\sqrt{3}) \\ & \Rightarrow \quad-\sqrt{3} y=-x+\sqrt{3} \\ & \Rightarrow \quad x-\sqrt{3} y=\sqrt{3} \\ & \Rightarrow \quad \sqrt{3} y=x-\sqrt{3} \end{aligned} $$
