JEE Main & Advanced Mathematics Straight Line Question Bank Critical Thinking

  • 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

    Correct Answer: A

    Solution :

               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\[\left( \frac{13}{5},0 \right)\].

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