Question

The equation of the line segment $AB$ is $y=x$. If $A$ and $B$ lie on the same side of the line mirror $2x-y=1$, then the image of $AB$ has the equation

• A. $x+y=2$
• B. $8x+y=9$
• C. $7x-y=6$
• D. None of these

Answer 1

Answer: (C)

We have, to find the locus of the point $(h,k)$ whose image on the line $2x-y-1=0$ lies on the line $y=x$.
Now, the image of $(h,k)$ on the line $2x-y-1=0$ is given by
$\frac{x_2-h}{2}=\frac{y_2-k}{-1}=-\frac{2(2h-k-1)}{5}$
or $x_2=\frac{-3h+4k+4}{5}$
and $y_2=\frac{4h+3k-2}{5}$
The point lies on $y=x$. Then,
$\frac{-3h+4k+4}{5}=\frac{4h+3k-2}{5}$
or $7h-k=6$