Fundamental Concepts
9. Collinear Points · When three points share one straight path
C lies on the line passing through A and B.
Three or more points are collinear when they all lie on the same straight line. Drag C along the line — AC + CB always equals AB, because C is between A and B on that single line.
What this lesson covers
Try to break it
Now drag C anywhere on the canvas. The moment it leaves line AB, the alignment breaks — A, B, C no longer line up and a triangle ABC appears in red.
How you build it
Place three collinear points.
- Place point A on the left.
- Place point B to the right of A.
- Draw line AB (Line tool: A then B).
- Place point C anywhere on line AB — it must sit on the line you just drew.
The proof, step by step
Prove that points A, B, and C are collinear.
- Points A and B define a unique straight line.
- Point C lies on this same line.
- Therefore, A, B, and C are collinear.
Worked example
Which of the following sets of points are collinear?
All three points sit on one straight line, so they're collinear. To check any three points, look at them and see if a single straight line can pass through all of them.
- (0,0), (1,1), (2,3)
- (0,0), (1,2), (2,4) — correct
- (0,0), (1,1), (3,1)
- (0,0), (2,1), (4,3)