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0606/12 May/Jun 2026, Question 2: Length of a Line Segment

Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 7 marks

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The question, in short

Given A(−2, 3) and B(8, −3), find c where the perpendicular bisector of AB meets C(0, c), and find integer n with D(2, −1) so that BD = (√n ÷ 2) AD.

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Part (a) · 3 marks

Find the value of c, given that the perpendicular bisector of AB passes through C(0, c).

  1. 1Gradient of AB = (−3 − 3)/(8 − (−2)) = −3/5
  2. 2Gradient of perpendicular bisector = 5/3
  3. 3Midpoint of AB = (3, 0)
  4. 4y = (5/3)(x − 3); at x = 0, y = −5
  5. 5c = −5

Answerc = −5

Part (b) · 4 marks

For D(2, −1), use the lengths AD and BD with BD = (√n ÷ 2) AD to find the integer n.

  1. 1AD² = (2 + 2)² + (−1 − 3)² = 32, AD = √32 = 4√2
  2. 2BD² = (8 − 2)² + (−3 + 1)² = 40, BD = √40 = 2√10
  3. 32√10 = (√n/2) × 4√2 = 2√(2n)
  4. 4√(2n) = √10, so n = 5

Answern = 5

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