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). Find the coordinates of the point A.

Answer 1

Let the incident ray strike X-axis at the point A, whose coordinates be (x,0).

From the figure, the slope of the reflected ray is given by

$tan\theta =\frac{3-0}{5-x}=\frac{3}{5-x}$



Again, the slope of the incident ray is given by

$tan(\pi -\theta )=\frac{0-2}{x-1}=\frac{-2}{x-1}$

$\Rightarrow -tan\theta =\frac{-2}{x-1}$

$\Rightarrow tan\theta =\frac{2}{x-1}$

On solving Eqs. (i) and (ii), we get

$\frac{3}{5-x}=\frac{2}{x-1}\Rightarrow 3x-3=10-2x\Rightarrow x=\frac{13}{5}$

Hence, the required coordinates of the point A are $(\frac{13}{5},0)$.