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0580/22 Feb/Mar 2025, Question 21: The Perpendicular Bisector

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 6 marks

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The question, in short

Find where the line y = 5x − 3 meets the y-axis, then find the perpendicular bisector equation of the line through A(1, 7) and B(5, 15) in y = mx + c form.

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Part (a) · 1 mark

State the coordinates of the y-axis intercept of y = 5x − 3.

  1. 1Crosses the y-axis when x = 0: y = 5 × 0 − 3 = −3
  2. 2(0, −3)

Answer(0, −3)

Part (b) · 5 marks

For A(1, 7) and B(5, 15), determine the perpendicular bisector's equation, expressed as y = mx + c.

  1. 1Midpoint of AB = ((1 + 5)/2, (7 + 15)/2) = (3, 11)
  2. 2Gradient of AB = (15 − 7)/(5 − 1) = 8/4 = 2
  3. 3Perpendicular gradient = −1/2
  4. 411 = −1/2 × 3 + c, so c = 11 + 3/2 = 25/2
  5. 5y = −(1/2)x + 25/2

Answery = −(1/2)x + 25/2

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Also searched as: 0580/22/F/M/25 · 0580_m25_qp_22 · 0580 m25 22 · question 21.
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