The mirror image of the point (1, 2, 3) in a plane is

$\left( { - {7 \over 3}, - {4 \over 3}, - {1 \over 3}} \right)$. Which of the following points lies on this plane ?

Let A(1, 2, 3), B$\left( { - {7 \over 3}, - {4 \over 3}, - {1 \over 3}} \right)$ <br><br>$\therefore$ Midpoint of AB = M = $$\left( {{{{{ - 7} \over 3} + 1} \over 2},{{{{ - 4} \over 3} + 2} \over 2},{{{{ - 1} \over 3} + 3} \over 2}} \right)$$ <br><br>= $\left( {{{ - 2} \over 3},{1 \over 3},{4 \over 3}} \right)$ <br><br>DR of AM = $\left( {1 + {2 \over 3},2 - {1 \over 3},3 - {4 \over 3}} \right)$ <br><br>= $\left( {{5 \over 3},{5 \over 3},{5 \over 3}} \right)$ <br><br>= (1, 1, 1) <br><br>Equation of plane <br><br>$$a\left( {x + {2 \over 3}} \right) + b\left( {y - {1 \over 3}} \right) + c\left( {z - {4 \over 3}} \right)$$ = 0 <br><br>$\Rightarrow$ $$1\left( {x + {2 \over 3}} \right) + 1\left( {y - {1 \over 3}} \right) + 1\left( {z - {4 \over 3}} \right)$$ = 0 <br><br>$\Rightarrow$ x + y + z = 1 <br><br>$\therefore$ (1, –1, 1) lies on the plane.