4MA1/2HR Jun 2018, Question 23: Vector Proofs
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks
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The question, in short
In triangle OAB with vectors OA = a and OB = b, C is midpoint of OA, D divides AB in ratio 3:1, and OB = 2BE. Using vectors, prove C, D, E are collinear.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1OD = a + 3/4(b − a) = 1/4a + 3/4b, and OC = 1/2a
- 2CD = OD − OC = 3/4b − 1/4a
- 3OE = b + 1/2b = 3/2b, so DE = 3/2b − (1/4a + 3/4b) = 3/4b − 1/4a
- 4CD = DE, so they are parallel and share point D
- 5CD = DE so C, D and E lie on the same straight line
AnswerCD = DE so C, D and E lie on the same straight line
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