The mirror image of the point $(1,2,3)$ in a plane is $\left(-\frac{7}{3},-\frac{4}{3},-\frac{1}{3}\right)$. Thus, the point lies on this plane.

• Correct answer
  A

  $(1,-1,1)$
• B

  $(-1,-1,1)$
• C

  $(1,1,1)$
• D

  $(-1,-1,-1)$

Solution

$\mathrm{M}$ is the midpoint. $$ \therefore \quad \mathrm{M} \equiv\left(-\frac{2}{3}, \frac{1}{3}, \frac{4}{3}\right) $$ D.r.s of $\mathrm{AB}$ are $\frac{-10}{3}, \frac{-10}{3}, \frac{-10}{3}$ i.e., $1,1,1$ Equation of plane is $$ \begin{aligned} & 1\left(x+\frac{2}{3}\right)+1\left(y-\frac{1}{3}\right)+1\left(z-\frac{4}{3}\right)=0 \\ & \Rightarrow x+y+z=1 \end{aligned} $$ Option (A) satisfies this equation of the plane.

Hence, the correct answer is option: 'A'.