Flash :: Reflection Of A Point Over A Line?

I have been looking at how to reflect a point in a line, and found this question which seems to do the trick, giving this formula to calculate the reflected point:

Given (x,y) and a line y = ax + c we want the point (x', y') reflected on the line.

Set d:= (x + (y - c)*a)/(1 + a^2)
Then x' = 2*d - x
and y' = 2*d*a - y + 2c

However there are two problems with this implementation for my needs:

My line is not described in the form y = ax + c (so I'd have to translate it, which is easy to do, but it means the process is slower). What if a is infinity ie. a vertical line?

Is there a simple way to calculate (x', y'), the reflection of point (x, y) in a line, where the line is described by the two points (x1, y1) and (x2, y2)?

Edit:

I've found a formula which does this, but it seems as though it does not work with lines that look like they have equation y = x.

Here it is in actionscript:

public static function reflect(p:Point, l:Line):Point
{
// (l.sx, l.sy) = start of line

[Code]....