4MA1/1HR Jun 2019, Question 24: Vector Geometry
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
Quadrilateral OABC has OA = a, OC = c, AB = 2c; P divides AB with AP : PB = 3 : 1. Using vectors, find the ratio AQ : QC where Q lies on AC and OQP is straight.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1AP = 3/4 × 2c = 3/2c, so OP = a + 3/2c
- 2Let AQ = n(c − a), so OQ = (1 − n)a + nc
- 3O, Q, P on a line, so OQ = k(a + 3/2c)
- 4Compare: 1 − n = k and n = 3/2k, so n = 3/2(1 − n), giving n = 3/5
- 5AQ = 3/5 AC, so AQ : QC = 3 : 2
Answer3 : 2
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