I studied this at school about a month ago. It isn't hard to understand, especially if you are not as bad as me. Let us start with a point (x,y) and a line, determined by the points (x1,y1) and (x2,y2). Now we need a determinant.
This is what we have now. To be honest, I do not know why the determinant is like that, so... I am sorry. It is not hard to remember the determinant itself, though.
Are you asking yourself what you should do with the determinant now, when you have it? Well, that is what we are supposed to do... First, we pick the first 2 columns and duplicate them onto the right side of the determinant. (figure 1)