Question

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

• A. 54
• B. 50
• C. -6
• D. -42

Answer 1

Answer: (C)

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