MCQ
A light ray emerging from the point source placed at $P( 1, 3)$ is reflected at a point $Q$ in the axis of $x$. If the reflected ray passes through the point $R$ ($6, 7)$, then the abscissa of $Q$ is
- A$1$
- B$3$
- C$\frac{7}{2}$
- ✓$\frac{5}{2}$
✓
Answer
Correct option: D.
$\frac{5}{2}$
d
Let abcissa of $Q=x$
Let abcissa of $Q=x$
$\therefore $ $Q=(x,0)$
$\tan \,\theta = \frac{{0 - 7}}{{x - 6}},\tan \left( {{{180}^o} - \theta } \right) = \frac{{0 - 3}}{{x - 1}}$
Now, $\tan \left( {{{180}^o} - \theta } \right) = - \tan \,\theta $
$\therefore \frac{{ - 3}}{{x - 1}} = \frac{{ - 7}}{{x - 6}} \Rightarrow x = \frac{5}{2}$
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