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4024/12 May/Jun 2025, Question 14: Pythagoras' Theorem

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 9 marks

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The question, in short

Given points A(−4, 5) and B(6, 1) with vector BC = (−3, −4), work out vectors and coordinates, then use trapezium ABCD with AB parallel to DC and AB = 2DC to find D and the length AD as a simplified surd.

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

Part (a) · 2 marks

Work out the column vector from A to B.

  1. 1→AB = (6 − (−4), 1 − 5)
  2. 2= (10, −4)

Answercolumn vector (10, −4)

Part (b) · 2 marks

Work out the coordinates of C.

  1. 1C = (6 + (−3), 1 + (−4))
  2. 2C = (3, −3)

Answer(3, −3)

Part (ci) · 2 marks

Using AB parallel to DC and AB = 2DC, work out the coordinates of D.

  1. 1→DC = 1/2 →AB = (5, −2)
  2. 2D = C − →DC = (3 − 5, −3 − (−2)) = (−2, −1)

Answer(−2, −1)

Part (cii) · 3 marks

Work out the length of AD, giving it as a surd in simplest form.

  1. 1AD² = (−2 − (−4))² + (−1 − 5)² = 2² + 6² = 40
  2. 2AD = √40 = √4 × √10 = 2√10

Answer2√10

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