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4024/22 May/Jun 2024, Question 11: The Perpendicular Bisector

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 10 marks

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The question, in short

Given Q(n, −4), R(−1, 8) and S(3, 2), work with distances, a ratio on a straight line, and a perpendicular bisector.

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

Part (a) · 3 marks

Using QR = 13, determine the two possible values of n.

  1. 1QR² = (n + 1)² + (−4 − 8)² = 13²
  2. 2(n + 1)² + 144 = 169, so (n + 1)² = 25
  3. 3n + 1 = ±5
  4. 4n = 4 or n = −6

Answer4 or −6

Part (b) · 2 marks

With RS : RT = 2 : 5 on straight line RST, work out the coordinates of T.

  1. 1→RS = (4, −6); RT = 5/2 × RS
  2. 2→RT = (10, −15)
  3. 3T = (−1 + 10, 8 − 15) = (9, −7)

Answer(9, −7)

Part (c) · 5 marks

Determine the equation of the line that perpendicularly bisects RS.

  1. 1Midpoint of RS = ((−1 + 3)/2, (8 + 2)/2) = (1, 5)
  2. 2Gradient RS = (2 − 8)/(3 − (−1)) = −6/4 = −3/2
  3. 3Perpendicular gradient = 2/3
  4. 45 = (2/3) × 1 + c, so c = 13/3
  5. 5y = (2/3)x + 4 1/3

Answery = (2/3)x + 4 1/3

Stuck on a step? Read the free lesson: The Perpendicular Bisector

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Also searched as: 4024/22/M/J/24 · 4024_s24_qp_22 · 4024 s24 22 · question 11.
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