Question

The equation of the image of line $y=x$ with respect to the line mirror $2x-y=1$ is

• A. $y=7x-5$
• B. $y=7x-6$
• C. $y=3x-7$
• D. $y=6x-5$

Answer 1

Answer: (B)

Image of $\left(0,0\right)$ w.r.t $L$ lies on $L_{1}$
Image of $\left(0,0\right)$ w.r.t $L$ is


$\frac{x - 0}{2}=\frac{y - 0}{- 1}=-2\left(\frac{- 1}{5}\right)$
$P^{'}\equiv \left(x , y\right)=\left(\frac{4}{5} , \frac{- 2}{5}\right)$
Equation of $L^{'}_{1}$ which passes through $\left(1,1\right)$ and $\left(\frac{4}{5} , \frac{- 2}{5}\right)$ is
$y-1=\frac{\frac{- 2}{5} - 1}{\frac{4}{5} - 1}\left(x - 1\right)=\frac{- 7}{- 1}\left(x - 1\right)$
$y=7x-6$