Prove the following


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:

  1. (1) 86

  2. (2) 88

  3. (3) 84

  4. (4) 90

Correct Option: , 2


$P(a, 6,9), Q(20, b,-a-9)$

mid point of $\mathrm{PQ}=\left(\frac{\mathrm{a}+20}{2}, \frac{\mathrm{b}+6}{2},-\frac{\mathrm{a}}{2}\right)$

lie on line




$18 a+252=14 a+28$




$\frac{b+2}{10}=-3 \Rightarrow b=-32$


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