Cambridge O Level Additional Mathematics · Syllabus 4037 · Vectors in Two Dimensions
Collinear Points
What is Collinear Points?
Three or more points that all lie on a single straight line. Using vectors, points A, B and C are collinear when one of the displacement vectors between them is a scalar multiple of another and the two displacements share a common point: for example AB equal to k times BC, with B belonging to both. The scalar multiple alone establishes only that the two segments are parallel, since parallel segments can lie on different lines; the shared point is what forces them onto the same line. A drawing that appears straight is never sufficient evidence, because diagrams in questions are not drawn to scale.
This definition is part of the Vectors in Two Dimensions chapter in Cambridge O Level Additional Mathematics.