Collinear

Definition

Points that lie on the same straight line.

Used by AQA, Edexcel and OCR

Specification G11 · Paper 1, Paper 2, Paper 3

Points are collinear if they lie on the same straight line.
Revise: Coordinate Geometry

Specification G11, G25 · Paper 1, Paper 2, Paper 3

To show that three non-vertical points are collinear, show that the gradient from the first point to the second equals the gradient from the second to the third. The two segments also share the middle point, so they form one straight line.
Revise: Coordinate Geometry Problems

1
For a proof, factorise the vectors being compared and finish with a sentence explaining why the lines are parallel or the points are collinear.
2
To prove points are collinear, compare vectors that share a point and state why the scalar-multiple relationship places the points on one straight line.

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Specification 9.03a · Paper 1 (Foundation), Paper 2 (Foundation), Paper 3 (Foundation), Paper 4 (Higher), Paper 5 (Higher), Paper 6 (Higher)

Describes points that lie on the same straight line.
Points are collinear when they lie on one straight line. To prove this using vectors, find two displacement vectors that share a point and show that one is a scalar multiple of the other.
Revise: Vector Operations