find the reflection of the point A(2,1) over the line 12x-5y-41=0

Answers (1)

:Solution: we have the given line 

L: 12x - 5y - 41 = 0      —    (1 )  slope (m)= 5 /12 

⇒ equation of the line passing through ( 2 ,1) and perpendicular to the given line 

⇒ ( y -1 ) = -5 /12( x - 2)

⇒     5x + 12y = 22    — (2)   

Now , intersection of the  line (1) and (2) is  (-4 ,7/2) 

let ( a,b) be the reflection point 

Then  ( a + 2) /2 = -4  and ( b +1 ) / 2 = 7/2 

  a = -10 And   b = 6

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