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0580/22 May/Jun 2023, Question 15: The Perpendicular Bisector

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 7 marks

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The question, in short

Using points C(5, −1) and D(13, 15), work out the midpoint, the gradient, and the perpendicular bisector equation in y = mx + c form.

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

Part (a) · 2 marks

Determine the coordinates halfway between C(5, −1) and D(13, 15).

  1. 1Midpoint = ((5 + 13)/2, (−1 + 15)/2)
  2. 2= (9, 7)

Answer(9, 7)

Part (b) · 2 marks

Work out the slope of the line joining C(5, −1) and D(13, 15).

  1. 1Gradient = (15 − (−1))/(13 − 5) = 16/8
  2. 2= 2

Answer2

Part (c) · 3 marks

Using C(5, −1) and D(13, 15), determine the line perpendicular to CD passing through its midpoint, giving y = mx + c.

  1. 1C(5, −1), D(13, 15): midpoint = ((5 + 13)/2, (−1 + 15)/2) = (9, 7)
  2. 2Gradient of CD = (15 − (−1))/(13 − 5) = 16/8 = 2
  3. 3Perpendicular gradient = −1/2
  4. 4Through (9, 7): 7 = −1/2 × 9 + c, so c = 23/2
  5. 5y = −(1/2)x + 23/2

Answery = −(1/2)x + 23/2

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Also searched as: 0580/22/M/J/23 · 0580_s23_qp_22 · 0580 s23 22 · question 15.
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