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4PM1/02R Jan 2022, Question 2: Equation of a Line Through Two Points

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 8 marks

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The question, in short

Using points A(−7, −1) and B(3, 4), find the line through them, then use C(−3, 7) and D(3, p) with AB = kAC and CD perpendicular to AB to find k and p.

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

Part (a) · 3 marks

Find the equation of the line through A(−7, −1) and B(3, 4), giving it as ax + by + c = 0 with integer coefficients.

  1. 1Gradient = (4 + 1)/(3 + 7) = 1/2
  2. 2y + 1 = ½(x + 7)
  3. 32y + 2 = x + 7
  4. 4x − 2y + 5 = 0

Answerx − 2y + 5 = 0

Part (b) · 2 marks

Given C(−3, 7) and AB = kAC, find the constant k.

  1. 1AB = √(10² + 5²) = 5√5
  2. 2AC = √(4² + 8²) = 4√5
  3. 3k = 5√5/(4√5) = 5/4

Answerk = 5/4

Part (c) · 3 marks

Given D(3, p) and that CD is perpendicular to AB, find the value of p.

  1. 1Gradient of CD = −2
  2. 2(7 − p)/(−3 − 3) = −2
  3. 37 − p = 12
  4. 4p = −5

Answerp = −5

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