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0580/23 May/Jun 2025, Question 24: The Gradient of a Straight Line

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 7 marks

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The question, in short

Work with coordinates of points A(a, 12) and B(b, 27), then use point D(22, 34) and E(23, 39) with 2CE = 5DE to locate C.

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

Part (ai) · 1 mark

Calculate the y-value halfway between the y-coordinates of A and B.

  1. 1y-coordinate of midpoint = (12 + 27)/2 = 19.5

Answer19.5

Part (aii) · 3 marks

Given the slope of AB equals 3, express a using b.

  1. 1Gradient = (27 − 12)/(b − a) = 3
  2. 215 = 3(b − a), so b − a = 5
  3. 3a = b − 5

Answerb − 5

Part (b) · 3 marks

Using the ratio 2CE = 5DE, determine the coordinates of point C.

  1. 1→DE = column vector (23 − 22, 39 − 34) = column vector (1, 5)
  2. 2CE = 5/2 DE, so →CE = column vector (2.5, 12.5)
  3. 3C = (23 − 2.5, 39 − 12.5) = (20.5, 26.5)

Answer(20.5, 26.5) or (41/2, 53/2)

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