How to bounce a point to hit a line with a certain angle

Question

I have a line and a point, line has an angle { angle } point has a velocity { x, y } , point moves to the line and hits it. At this point I want to change the velocity of the point, as if the point bounces from the line with regard to the line angle. How do I calculate the new velocity of the point based on line angle?

Answer 1

No 'gravity'? Perfect elasticity?

a = angle
b = atan(y/x)  -- angle of 'velocity'
c = 2a-b       -- angle of new velocity
r = sqrt(x*x + y*y)  --  scaling of x,y
v = r * cos(c)
w = r * sin(c)
new velocity = {v, w}

(Caveat: I don't know what a is relative to - vertical or horizontal, nor which direction. And there may be other issues.)