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4024/11 May/Jun 2020, Question 18: Pythagoras' Theorem

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

On a 1 cm grid, quadrilateral PQRS has vertices P(4, 3), Q(−2, −3), R(−5, 2), S(−2, 5). Identify the shape, find the midpoint of QR, and find m where PS = √m cm.

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

Part (a) · 1 mark

Name the special quadrilateral PQRS shown on the grid.

  1. 1PQ has gradient 6/6 = 1 and SR has gradient 3/3 = 1, so PQ ∥ SR
  2. 2Only one pair of parallel sides: trapezium

AnswerTrapezium

Part (b) · 1 mark

Calculate the coordinates of the midpoint of the side QR.

  1. 1Midpoint of QR = ((−2 + −5)/2, (−3 + 2)/2)
  2. 2= (−3 1/2, −1/2)

Answer(−3 1/2, −1/2)

Part (c) · 2 marks

Given PS has length √m cm, determine the value of m.

  1. 1From S(−2, 5) to P(4, 3): across 6, down 2
  2. 2PS² = 2² + 6² = 4 + 36 = 40
  3. 3PS = √40, so m = 40

Answer40

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