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4PM1/01R Jan 2022, Question 3: The Perpendicular Bisector

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 10 marks

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The question, in short

Given A(1, 7) and B(9, 3), with line l the perpendicular bisector of AB, find an equation of l and then the area of triangle ABC where l meets the x-axis at C.

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

Part (a) · 5 marks

Find an equation of the line l, the perpendicular bisector of segment AB joining (1, 7) and (9, 3).

  1. 1Midpoint of AB = (5, 5)
  2. 2Gradient of AB = (3 − 7)/(9 − 1) = −1/2
  3. 3Gradient of l = 2
  4. 4y − 5 = 2(x − 5)
  5. 5y = 2x − 5

Answery = 2x − 5

Part (b) · 5 marks

Line l crosses the x-axis at C; find the area of triangle ABC.

  1. 1y = 0: x = 5/2, so C = (5/2, 0)
  2. 2Distance from C to the midpoint (5, 5) = √(2.5² + 5²) = 5√5/2
  3. 3AB = √(8² + 4²) = 4√5
  4. 4Area = ½ × 4√5 × 5√5/2 = 25

Answer25

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