Question

A ray of light coming from the point (1, 2) is reflected at a point A on the x - axis and then passes through the point (5, 3). The coordinates of the point A are

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Let the coordinates of A be (a, 0). Then the slope of the reflected ray is $\frac{3-0}{5-a}=tan\theta$, (say)
The slope of the incident ray = $\frac{2-0}{1-a}tan(\pi -\theta )$
Since $tan\theta +tan(\pi -\theta )=0\Rightarrow \frac{3}{5-a}+\frac{2}{1-a}=0$
$\Rightarrow 13-5z=0\Rightarrow a=\frac{13}{5}$
Thus the coordinates of A are $(\frac{13}{5},0)$