ANSWER: ( -3 , -6 )
We know that ,
The formula for the reflection of (x1 , y1) in the line ax + by + c = 0 is
\({x - {x}_{1} \over a } = {y - {y}_{1} \over b} ={ -2(a{x}_{1} + b{y}_{1} + c) \over {a}^{2} + {b}^{2}}\)
Here we have
( x1 , y1 ) → ( 1 , 2 )
ax + by + c = 0 → x + 2y + 5 = 0
( x , y ) → Image
Substituting in above equation
\({x - 1 \over 1} = { y - 2 \over 2} ={ -2(1 + 2(2) + 5 )\over{1}^{2}+{2}^{2}}\)
\(x - 1 = { -2(1+4+5)\over 5}\)
\(x - 1 = - 4 \)
\(x = - 3 \)
Similarly
\({y-2\over2} = - 4 \)
y - 2 = - 8
y = - 6
\(\therefore\) The image of point (1,2) about the line x + 2x + 5 = 0 is ( -3 , - 6 ).