Checking to see if 3 points are on the same line

Question

I want to know a piece of a code which can actually tell me if 3 points in a 2D space are on the same line or not. A pseudo-code is also sufficient but Python is better.

Answer 1

You can check if the area of the ABC triangle is 0:

[ Ax * (By - Cy) + Bx * (Cy - Ay) + Cx * (Ay - By) ] / 2 

Of course, you don't actually need to divide by 2.

Answer 2

This is C++, but you can adapt it to python:

bool collinear(int x1, int y1, int x2, int y2, int x3, int y3) {   return (y1 - y2) * (x1 - x3) == (y1 - y3) * (x1 - x2); } 

Basically, we are checking that the slopes between point 1 and point 2 and point 1 and point 3 match. Slope is change in y divided by change in x, so we have:

y1 - y2     y1 - y3 -------  =  -------- x1 - x2     x1 - x3 

Cross multiplying gives (y1 - y2) * (x1 - x3) == (y1 - y3) * (x1 - x2);

Note, if you are using doubles, you can check against an epsilon:

bool collinear(double x1, double y1, double x2, double y2, double x3, double y3) {   return fabs((y1 - y2) * (x1 - x3) - (y1 - y3) * (x1 - x2)) <= 1e-9; }