Question

If the mirror image of the point $(2,4,7)$ in the plane $3x-y+4z=2$ is $(a,b,c)$, the $2a+b+2c$ is equal to :

• A. 54
• B. 50
• C. -6
• D. -42

Answer 1

Answer: (C)

$\frac{a-2}{3}=\frac{b-4}{-1}=\frac{c-7}{4}=\frac{-2(6-4+28-2)}{3^2+1^2+4^2}$
$\Rightarrow a=\frac{-84}{13}+2,b=\frac{28}{13}+4,C=\frac{-112}{13}+7$
$\Rightarrow 2a+b+2c=-6$