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