Proving Three Points Are Collinear
Part of Vectors (Geometry Proofs) · GCSE GCSE Mathematics revision
This deep dive covers Proving Three Points Are Collinear within Vectors (Geometry Proofs) for GCSE Mathematics. Revise Vectors (Geometry Proofs) in Geometry & Measures for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 8 of 12 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 8 of 12
Practice
14 questions
Recall
12 flashcards
Proving Three Points Are Collinear
Three points A, B, C are collinear (lie on the same straight line) if:
- Vector AB is parallel to vector BC (a scalar multiple), AND
- They share a common point (point B).
Both conditions are needed. Parallel alone is not enough — the vectors could be on separate parallel lines.
Method:
- Find AB and BC (or AC) in terms of a and b.
- Show AB = k × BC for some scalar k.
- State that since AB and BC are parallel and share point B, A, B, C are collinear.
Keep building this topic
Read this section alongside the surrounding pages in Vectors (Geometry Proofs). That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Vectors (Geometry Proofs)
Vector AB goes from point A to point B. Which of the following describes vector BA?
A student says: 'I have shown that vector AB is parallel to vector CD, so A, B, C, D all lie on the same straight line.' Explain why the student's reasoning is incorrect.
Quick Recall Flashcards
14 questions on Vectors (Geometry Proofs) — practise free
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