Question

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. $\frac{7}{2}$
• D. $\frac{5}{2}$

Answer 1

Answer: (D)

$\frac{5}{2}$

Answer 2

Let abcissa of $Q = x$
$\therefore Q = \left(x, 0\right)$
$tan\,\theta = \frac{0-7}{x-6}, tan \left(180^{\circ}-\theta\right) = \frac{0-3}{x-1}$
Now, tan $\left(180^{\circ}- \theta\right)=- tan \,\theta$
$\therefore\quad \frac{-3}{x-1} = \frac{-7}{x-6} \Rightarrow x = \frac{5}{2}$