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4024/21 May/Jun 2022, Question 11: The Perpendicular Bisector

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks

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The question, in short

Given points P (3, −3) and Q (1, 5), work out the distance between them and then determine the line that cuts PQ in half at right angles.

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

Part (a) · 2 marks

Work out how far apart P (3, −3) and Q (1, 5) are.

  1. 1PQ² = (3 − 1)² + (−3 − 5)² = 4 + 64 = 68
  2. 2PQ = √68 = 8.246… ≈ 8.25

Answer8.25 or 8.246…

Part (b) · 5 marks

Determine the equation of the line that passes through the midpoint of P (3, −3) and Q (1, 5) and is at right angles to PQ.

  1. 1Midpoint of PQ = ((3 + 1)/2, (−3 + 5)/2) = (2, 1)
  2. 2Gradient PQ = (5 − (−3))/(1 − 3) = 8/(−2) = −4
  3. 3Perpendicular gradient = 1/4
  4. 41 = (1/4) × 2 + c, so c = 1/2
  5. 5y = (1/4)x + 1/2

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

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

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Also searched as: 4024/21/M/J/22 · 4024_s22_qp_21 · 4024 s22 21 · question 11.
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