Let's say you have a two dimensional plane with 2 points (called a and b) on it represented by an x integer and a y integer for each point.
How can you determine if another point c is on the line segment defined by a and b?
I use python most, but examples in any language would be helpful.
Check if the cross product of (b-a) and (c-a) is 0, as tells Darius Bacon, tells you if the points a, b and c are aligned.
But, as you want to know if c is between a and b, you also have to check that the dot product of (b-a) and (c-a) is positive and is less than the square of the distance between a and b.
In non-optimized pseudocode:
def isBetween(a, b, c): crossproduct = (c.y - a.y) * (b.x - a.x) - (c.x - a.x) * (b.y - a.y) if abs(crossproduct) > epsilon : return False # (or != 0 if using integers) dotproduct = (c.x - a.x) * (b.x - a.x) + (c.y - a.y)*(b.y - a.y) if dotproduct < 0 : return False squaredlengthba = (b.x - a.x)*(b.x - a.x) + (b.y - a.y)*(b.y - a.y) if dotproduct > squaredlengthba: return False return True