The line L: (x-1)/(2)=(y-2)/(-1)=(z)/(-1) is reflected in the plane Pi passing through the points (9,0,0), (0,9,0) and (0,0,9). The shortest distance…

The plane through the three given points is $x+y+z=9$ with normal $(1,1,1)$. The direction of $L$ is $(2,-1,-1)$ and $(2,-1,-1)\cdot(1,1,1)=0$, so $L$ is parallel to $\Pi$. The image line is therefore parallel to $L$ and lies at the same distance on the other side of the plane. The point $(1,2,0)$ on $L$ has distance $\dfrac{|1+2+0-9|}{\sqrt3}=\dfrac{6}{\sqrt3}=2\sqrt3$ from $\Pi$. Hence the distance between $L$ and its image is twice this, $4\sqrt3\approx 6.93$. The option $2\sqrt3$ is only the distance of $L$ from the mirror, a common slip.