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4MA1/1H Jun 2018, Question 17: Position Vectors

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks

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The question, in short

Parallelogram ABCD with vectors AB = (2, 7) and AC = (10, 11), B at (5, 8). Find C's coordinates, then use vectors to show A, B, E are collinear for E (63, 211).

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

Part (a) · 3 marks

Work out the coordinates of point C using the given vectors and point B.

  1. 1A = B − AB→ = (5 − 2, 8 − 7) = (3, 1)
  2. 2C = A + AC→ = (3 + 10, 1 + 11)
  3. 3C = (13, 12)

Answer(13, 12)

Part (b) · 2 marks

Using a vector method, prove that points A, B and E lie on a straight line.

  1. 1BE→ = (63 − 5, 211 − 8) = (58, 203)
  2. 258 = 29 × 2 and 203 = 29 × 7, so BE→ = 29 AB→
  3. 3BE→ is parallel to AB→ and they share point B
  4. 4So A, B and E lie on one straight line — proof

AnswerProof

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