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A ray of light is incident along a line which meets another line, 7x − y + 1 = 0, at the point (0, 1). The ray is then reflected from this point along the line, y + 2x = 1. Then the equation of the line of incidence of the ray of light is :
Option: 1
41x − 38y + 38 = 0

Option: 2
41x + 25y − 25 = 0

Option: 3
41x + 38y − 38 = 0

Option: 4
41x − 25y + 25 = 0

Answers (1)

best_answer

$\\Let \:slope\: of\: incident\: ray\: is \:m\\\therefore angle\:of\:incident\:=angle\:of\:reflection\\\therefore \left|\frac{m-7}{1+7m}\right|=\left|\frac{-2-7}{1-24}\right| =\frac{9}{13}\\\frac{m-7}{1+7m}=\frac{9}{13\:}\:\:\:or\:\:\:\frac{m-7}{1+7m}=-\frac{9}{13}\\\Rightarrow m=-\frac{1}{2}\:\:or\:\:m=\frac{41}{38}\\\Rightarrow \left(y-1\right)=-\frac{1}{2}\left(x-0\right)\:\:or\:\:\left(y-1\right)=\frac{41}{38}\left(x-0\right)\\i.e.x+2y-2=0\:\:or\:38y-41x-38=0\\ans\:is\:\:38y-41x-38=0$

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