Coordinate Geometry
Straight Lines
MMTS_Full_Test_12
Grade 12

Question:

A ray of light along $x+\sqrt{3}y=\sqrt{3}$ gets reflected upon reaching $x$-axis. The equation of the reflected ray is
$y=x+\sqrt{3}$
$\sqrt{3}y=x-\sqrt{3}$
$y=\sqrt{3}x-\sqrt{3}$
$\sqrt{3}y=x-1$

Step-by-Step Solution

Key Concept: Reflect the slope about $x$-axis: if slope $m$, reflected slope $=-m$
$x+\sqrt{3}y=\sqrt{3}$: when $y=0$, $x=\sqrt{3}$. Point $=(\sqrt{3},0)$. Slope of incident $=-1/\sqrt{3}$. Reflected slope $=1/\sqrt{3}$. Reflected ray: $y=\frac{1}{\sqrt{3}}(x-\sqrt{3})\Rightarrow\sqrt{3}y=x-\sqrt{3}$.
Correct Answer: 3

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