A light beam, emanating from the point (3,10) reflects from the straight line `2x+y - 6 = 0` and, then passes through the point (7,2) .Find the equations of the incident and reflected beams .

Explanation

Let images of P and R about the line `2x+y-6=0` be `P(x_(1),y_(1)) and R(x_(2),y_(2))` respecftively. Then
`(x_(1)-3)/(2)=(y_(1)-10)/(1)=(-2(6+10-6))/(2^(2)+1^(2))=-4`
`x_(1)=-5,y_(1)=6impliesP'(-5,6)`
`and (x_(2)-7)/(2)=(y_(2)-2)/(1)=(-2(14+2-6))/(2^(2)+1^(2))=-4`
`impliesx_(2)=-1,y_(2)=-2impliesR'(-1,-2)`

`therefore` Equation of inclident ray PR' is
`y+2=(10+2)/(3+1)(x+1)`
`implies3x-y+1=0`
and equation of reflected ray RP' is
`y-6=(2-6)/(7+5)(x+5)`
`impliesx+3y-13=0`