The reflection of the point (4,-13) in the S.L 5x+y+6=0 is the point??

Dear anand s

let the reflection is (h,k)

mid point of (h,k) and (4,-13) lies on straight line

and slope of line and the line joining by point(h,k) and (4,-13) are perpendicular

slope of the line =-5

slope of line  joining by point(h,k) and (4,-13)=(k+13)/(h-4)

so (k+13)/(h-4) * (-5) =-1

 5k +65 =h-4

or  h= 5k +69 ......1

 

and mid point lie on line

so 5(h+4)/2   + (k-13)/2   +6  = 0

 or 5(h+4)   + (k-13)   +12  = 0

     5h + k +19 =0..............2

solve above  two equation

point(-1 ,-14)

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