Algorithm for reflecting a point across a line

Question

Given a point (x1, y1) and an equation for a line (y=mx+c), I need some pseudocode for determining the point (x2, y2) that is a reflection of the first point across the line

Answer 1

Reflection of point in the line Given point P(x,y) and a line L1 Then P(X,Y) is the reflected point on the line L1 If we join point P to P’ to get L2 then gradient of L2=1/m1 where m1 is gradient of L1 L1 and L2 are perpendicular to each other Get the point of intersection of L1 and L2 say m(a,b) Since m(a,b) is the midpoint of PP’ i.e. L2, then M=
i.e. = from this we can get coordinates of Example Find the image of point P(4,3) under a reflection in the line
M1=1 M2 will be -1 Equ. L2 with points, (4,3) , (x ,y) grad -1 is

Point of intersection say, M(a ,b) Note that, L1 =L2 ; Then This gives the point for M that is M( 6,1) Then;

          This gives x = 8 and y = -1 hence,

P'(x,y) = P'(8,-1)