Lemmara logoLemmaraWorked solution

4MA1/2H Jun 2020, Question 19: Vector Proofs

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 3 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Triangle OAB has vectors OA = a and OB = b. Points C and D divide OA and OB in ratio 1:2. Use vectors to prove ABDC is a trapezium.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Solution · 3 marks

  1. 1AB→ = −a + b = b − a
  2. 2OC→ = ⅓a and OD→ = ⅓b
  3. 3CD→ = −⅓a + ⅓b = ⅓(b − a) = ⅓AB→
  4. 4CD is a multiple of AB, so they are parallel
  5. 5AB and CD are parallel therefore ABDC is a trapezium

AnswerAB and CD are parallel therefore ABDC is a trapezium

Stuck on a step? Read the free lesson: Vector Proofs

Practise more vector proofs questions

Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on vector proofs

Also searched as: 4MA1 2H June 2020 · 4MA1/2H · 4ma1 jun20 2h · question 19.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.