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4024/22 May/Jun 2022, Question 10: Length of a Line Segment

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 12 marks

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The question, in short

Coordinate geometry with D(4, 6): find E(e, e) from a distance of √20, then use a perpendicular bisector of gradient 3/2 to find f and the constant k.

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

Part (a) · 5 marks

Use the distance formula to form and solve a quadratic in e.

  1. 1(e − 4)² + (e − 6)² = 20
  2. 2e² − 8e + 16 + e² − 12e + 36 = 20
  3. 32e² − 20e + 32 = 0, so e² − 10e + 16 = 0
  4. 4(e − 2)(e − 8) = 0, so e = 2 or e = 8
  5. 5E is (2, 2) or (8, 8)

Answer(2, 2) and (8, 8)

Part (bi) · 4 marks

Gradient of DF is −2/3 since the bisector is perpendicular: find f.

  1. 1Gradient DF = −1 ÷ 3/2 = −2/3
  2. 2(5f − 6)/(−f − 4) = −2/3
  3. 33(5f − 6) = −2(−f − 4)
  4. 415f − 18 = 2f + 8, so 13f = 26
  5. 5f = 2

Answer2

Part (bii) · 3 marks

Put the midpoint of DF into 2y = 3x + k to find k.

  1. 1F = (−2, 10)
  2. 2Midpoint of DF = ((4 − 2)/2, (6 + 10)/2) = (1, 8)
  3. 32 × 8 = 3 × 1 + k
  4. 4k = 13

Answer13

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Also searched as: 4024/22/M/J/22 · 4024_s22_qp_22 · 4024 s22 22 · question 10.
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