4PM1/02R Jun 2025, Question 1: Vector Proofs
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 4 marks
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The question, in short
Given vectors AB = 3a + 2b, AD = 2a − 5b and AC = 5a − 3b for quadrilateral ABCD, show that ABCD is a parallelogram.
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Solution · 4 marks
- 1BC = BA + AC = −3a − 2b + 5a − 3b = 2a − 5b
- 2DC = DA + AC = −2a + 5b + 5a − 3b = 3a + 2b
- 3BC = AD and DC = AB
- 4Opposite sides are equal and parallel, so ABCD is a parallelogram
AnswerBC = 2a − 5b = AD (and DC = 3a + 2b = AB), so ABCD is a parallelogram
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