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


$\frac{x-0}{2}=\frac{y-0}{-1}=-2\left(\frac{-1}{5}\right)$
$P^{{}^{\prime }}\equiv \left(x,y\right)=\left(\frac{4}{5},\frac{-2}{5}\right)$
Equation of $L_1^{{}^{\prime }}$ which passes through $\left(1,1\right)$ and $\left(\frac{4}{5},\frac{-2}{5}\right)$ is
$y-1=\frac{\frac{-2}{5}-1}{\frac{4}{5}-1}\left(x-1\right)=\frac{-7}{-1}\left(x-1\right)$
$y=7x-6$