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ANSWER:  ( -3 , -6 )

We know that , 

The formula for the reflection of (x, 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 ).

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