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4024/12 Oct/Nov 2022, Question 16: The Gradient of a Straight Line

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Given points P(−2, 1) and Q(6, 13), with M the midpoint of PQ, find M's coordinates, the gradient of PQ, and the gradient of a perpendicular line.

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

Part (a) · 1 mark

Find the coordinates of the midpoint M of the line segment joining P(−2, 1) and Q(6, 13).

  1. 1M = ((−2 + 6)/2, (1 + 13)/2)
  2. 2M = (2, 7)

Answer(2, 7)

Part (bi) · 2 marks

Find the gradient of the line passing through P(−2, 1) and Q(6, 13).

  1. 1Gradient = (13 − 1)/(6 − (−2))
  2. 2= 12/8 = 3/2

Answer3/2

Part (bii) · 1 mark

Write down the gradient of a line perpendicular to PQ, using the gradient found in part (i).

  1. 1Gradient of PQ = (13 − 1)/(6 − (−2)) = 12/8 = 3/2
  2. 2Perpendicular gradients multiply to −1
  3. 3Perpendicular gradient = −1 ÷ 3/2 = −2/3

Answer−2/3

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