What algorithm or formula can be used to find out if a point is between parallel lines?

Question

Mathematics

There are two parallel lines given by the equation a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0
How to determine if the point P(x, y) is between them?

Answer 1

Calculate (a1*x + b1*y + c1)*(a2*x + b2*y + c2). If its sign is the same as that of a1*a2+b1*b2, then the point belongs to an obtuse angle between the lines, if the other - then to an acute one. In the case of parallel or almost parallel lines, the second case corresponds to the situation "lies between", and the first - "not".