Official solution
Given, P(a, 6, 9)
Equation of line \[{{x - 3} \over 7} = {{y - 2} \over 5} = {{z - 1} \over { - 9}}\]
Image of point P with respect to line is point Q(20, b, -a -9)
Mid-point of P and Q = \[\left( {{{a + 20} \over 2},{{6 + b} \over 2},{{ - a} \over 2}} \right)\]
This point lies on line
\[\therefore\] \[{{{{a + 20} \over 2} - 3} \over 7} = {{{{6 + b} \over 2} - 2} \over 5} = {{{{ - a} \over 2} - 1} \over { - 9}}\]
\[ \Rightarrow {{a + 14} \over {14}} = {{b + 2} \over {10}} = {{a + 2} \over {18}}\]
\[ \Rightarrow {{a + 14} \over {14}} = {{a + 2} \over {18}}\] and \[{{b + 2} \over {10}} = {{a + 2} \over {18}}\]
Solving, we get a = - 56, b = - 32
\[\therefore\] \[\left| {a + b} \right| = \left| { - 56 - 32} \right| = 88\]