Question

A ray of light is sent along the line $x-2y-3=0$. Upon reaching the line $3x-2y-5=0$ the ray is reflected from it. The equation of the reflected ray is

• A. $13x-y=14$
• B. $17x-2y=19$
• C. $29x-2y=31$
• D. $x+y=11$

Answer 1

The correct option is C $29x-2y=31$

Incident ray : $x-2y-3=0$
Line mirror : $3x-2y-5=0$
Solving these two equation , $P(1,-1)$

Let $A^{\prime }(\alpha ,\beta )$ be the image of $A(3,0)$
w.r.t $3x-2y-5=0$
$\Rightarrow$ $\frac{\alpha -3}{3}=\frac{\beta -0}{-2}=\frac{-2(9-0-5)}{5}$$\Rightarrow A^{\prime }=(\frac{15}{13},\frac{16}{13})$
$\therefore$ Equation of $P{A}^{\prime }$(reflected ray) is $29x-2y-31=0$