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4024/22 Oct/Nov 2025, Question 18: The Perpendicular Bisector

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 9 marks

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The question, in short

For line L with equation y = x/5 + 3 and parallel line M through A(15, 0) and B on the y-axis, find the gradient, show B's coordinates, and find where perpendicular bisector N meets the x-axis at C.

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

Part (a) · 1 mark

State the gradient of line L from its equation.

  1. 1y = x/5 + 3 is in the form y = mx + c, so gradient = 1/5

Answer1/5

Part (bi) · 3 marks

Using that M is parallel to L and passes through A(15, 0), show that B is (0, −3).

  1. 1M is parallel to L, so M: y = x/5 + c
  2. 2Through A(15, 0): 0 = 15/5 + c = 3 + c
  3. 3c = −3, so B = (0, −3)

AnswerCorrect working leading to (0, −3)

Part (bii) · 5 marks

Find the coordinates of C, where line N, the perpendicular bisector of AB, crosses the x-axis.

  1. 1Midpoint of AB = ((15 + 0)/2, (0 + (−3))/2) = (7.5, −1.5)
  2. 2Gradient of N = −1 ÷ 1/5 = −5
  3. 3−1.5 = −5 × 7.5 + c, so c = 36: y = −5x + 36
  4. 4At C, y = 0: 5x = 36, x = 7.2
  5. 5C = (7.2, 0)

Answer(7.2, 0)

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Also searched as: 4024/22/O/N/25 · 4024_w25_qp_22 · 4024 w25 22 · question 18.
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