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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 co-ordinates of the point A are ____

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

$(- 7, 0)$

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

$(15, 0)$

answer is C.

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Detailed Solution

$\tan θ = \frac{3}{5 - x}; \tan (θ) = \frac{2}{1 - x}$

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

$\Rightarrow x = \frac{13}{5}$

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