Question

Let $a,b\in R$. If the mirror image of the point $P(a$, 6,9) with respect to the line
$\frac{x-3}{7}=\frac{y-2}{5}=\frac{z-1}{-9}$ is $(20,b,-a-9),$ then $|a+b|$ is equal to:

• A. 88
• B. 86
• C. 84
• D. 90

Answer 1

Answer: (A)

$P(9,6,9)$
$\frac{x-3}{7}=\frac{y-2}{5}=\frac{z-1}{-9}$
$Q=(20,b,-a-9)$
$\frac{\frac{20+a}{2}-3}{7}=\frac{\frac{b+6}{2}-2}{5}=\frac{-\frac{9}{2}-1}{-9}$
$\frac{14+9}{14}=\frac{b+2}{10}=\frac{a+2}{18}$
$\Rightarrow a=-56$ and $b=-32$
$\Rightarrow |a+b|=88$