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4024/12 Oct/Nov 2025, Question 8: The Gradient of a Straight Line

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Use a grid with points A and B shown and B at (4, 3) to read A's coordinates, find p for C(p, −1) with gradient BC = −2, then locate D of parallelogram ABCD.

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

Part (a) · 1 mark

State the coordinates of point A as read from the grid.

  1. 1A = (−2, 1)

Answer(−2, 1)

Part (b) · 2 marks

Given C is (p, −1) and the gradient of BC is −2, determine the value of p.

  1. 1Gradient BC = (−1 − 3)/(p − 4) = −2
  2. 2−4 = −2(p − 4)
  3. 3p − 4 = 2, so p = 6

Answer6

Part (c) · 2 marks

Using AB and BC as adjacent sides of parallelogram ABCD, find the coordinates of D.

  1. 1→BC = C − B = (6 − 4, −1 − 3) = column vector (2, −4)
  2. 2→AD = →BC, so D = (−2 + 2, 1 − 4)
  3. 3D = (0, −3)

Answer(0, −3)

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