• # question_answer 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                                            [Orissa JEE 2003] A) $\left( 13/5,\ 0 \right)$         B) $\left( 5/13,\ 0 \right)$C) (- 7, 0)                                       D) None of these

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