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:
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Official solution
Let slope of incident ray be m.
\[ \therefore \] angle of incidence = angle of reflection
\[ \therefore \] \[\left| {{{m - 7} \over {1 + 7m}}} \right| = \left| {{{ - 2 - 7} \over {1 - 14}}} \right| = {9 \over {13}}\]
\[ \Rightarrow \] \[{{m - 7} \over {1 + 7m}} = {9 \over {13}}\]
or \[{{m - 7} \over {1 + 7m}} = - {9 \over {13}}\]
\[ \Rightarrow \] 13m - 91 = 9 + 63m
or 13m - 91 = - 9 - 63m
\[ \Rightarrow \] 50m = - 100 or 76m = 82
\[ \Rightarrow \] m = \[ - {1 \over 2}\]
or m = \[{{41} \over {38}}\]
\[ \Rightarrow \] y - 1 = - \[{1 \over 2}\] (x - 0)
or y - 1 = \[{{41} \over {38}}\] (x - 0)
i.e x + 2y - 2 = 0
or 38y - 38 - 41x = 0
\[ \Rightarrow \] 41x - 38y + 38 = 0