Straight Line Question 59

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 [Orissa JEE 2003]

Options:

A) $ ( 13/5,\ 0 ) $

B) $ ( 5/13,\ 0 ) $

C) (- 7, 0)

D) None of these

Show Answer

Answer:

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 ,(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 $ ( \frac{13}{5},0 ) $ .