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  4. 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 his point along the line, y + 2x = 1. Then the equation of the line of incidence of the ray of light is :

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Q. 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 his point along the line, $y + 2x = 1$. Then the equation of the line of incidence of the ray of light is :

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Solution:

Incidene line
$L _{1}+\lambda L _{2}=0$
$(7 x-y+1)+\lambda(v+2 x-1)=0$
image
Let a point $(1,-1)$ on $y+2 x=1$
And image of $(1,-1)$ lie on incidence line in
$7 x-v+1=0$
$\frac{x-1}{1}=\frac{y+1}{-1}=\frac{-2(7+1+1)}{50}=x=\frac{-38}{25}, \quad y=\frac{-16}{25}$
$\left(7\left(\frac{-38}{25}\right)+\frac{16}{25}+1\right)+\lambda\left(\frac{-16}{25}-\frac{76}{25}-1\right)$
$\lambda=\frac{-225}{117}$
$(7 x-y+1) \frac{-225}{117}(y+2 x-1)=0$
$369 x-342 y+342=0$
$41 x-38 y+38=0$