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Geometry & MeasuresKey Facts

Key Results to Remember

Part of Vectors (Geometry Proofs) — GCSE Mathematics

This key facts covers Key Results to Remember 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 9 of 11 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 9 of 11

Practice

14 questions

Recall

12 flashcards

Key Results to Remember

  • Midpoint: OM = ½(OA + OB) — always the average of the two position vectors.
  • Parallel test: p parallel to q if and only if p = kq (k is a non-zero scalar).
  • Collinear test: Parallel vectors + common point = collinear points.
  • Ratio m:n: fraction of the way along = m/(m+n).
  • Direction only: two vectors being parallel says nothing about their position — always note the shared point when proving collinearity.

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.

Points Dividing a Line in a Given RatioExam TipsVectors in Geometry: Proving What You Can SeeVector Notation Recap

Practice Questions for Vectors (Geometry Proofs)

Vector AB goes from point A to point B. Which of the following describes vector BA?

  • A. The same vector as AB
  • B. Twice the length of AB in the same direction
  • C. The same magnitude as AB but in the opposite direction
  • D. Half the length of AB in the opposite direction
1 markfoundation

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.

2 marksstandard

Quick Recall Flashcards

If AB = a, what is BA?
BA = -a. Reversing the direction of travel negates the vector. In diagrams: if you travel against an arrow, write a negative sign in front of that vector.
When are two vectors parallel?
Two vectors p and q are parallel when one is a scalar multiple of the other: p = kq for some non-zero scalar k. They point in the same or exactly opposite direction.

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