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4MA1/2H Jan 2020, Question 23: Vector Geometry

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

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The question, in short

In triangle ABC, M is the midpoint of BC and P lies on AM. Given vectors AB = 4a, AC = 2b and AP = (3/2)a + (3/4)b, work out the ratio AP : PM.

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

Solution · 3 marks

  1. 1PM → = AM → − AP →
  2. 2AM → = (AB → + AC →)/2 = (4a + 2b)/2 = 2a + b
  3. 3AP → = (3/2)a + (3/4)b
  4. 4PM → = (2a + b) − ((3/2)a + (3/4)b) = (2 − 3/2)a + (1 − 3/4)b = (1/2)a + (1/4)b
  5. 5AP → : PM → = ((3/2)a + (3/4)b) : ((1/2)a + (1/4)b)
  6. 6Factor out (1/4): AP → = (6a + 3b)/4, PM → = (2a + b)/4
  7. 7Ratio = (6a + 3b) : (2a + b) = 3(2a + b) : (2a + b) = 3 : 1

Answer3 : 1

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