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4PM1/02R Jan 2023, Question 5: Area of a Triangle

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 11 marks

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The question, in short

Line l has gradient −1/12 and goes through A(p, 10) and B(123, 0); work with l and the perpendicular line k through A to find p, equations, and the area of triangle ABC.

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

Part (a) · 2 marks

Use the gradient formula with the two points and gradient −1/12 to show that p = 3.

  1. 1Gradient: −1/12 = (10 − 0)/(p − 123)
  2. 2p − 123 = −120
  3. 3p = 3

Answerp = 3 shown

Part (b) · 2 marks

Find l's equation in the integer form rx + sy + t = 0.

  1. 1y − 10 = −(1/12)(x − 3)
  2. 212y − 120 = −x + 3
  3. 3x + 12y − 123 = 0

Answerx + 12y − 123 = 0

Part (c) · 3 marks

Find the equation of k, perpendicular to l through A, in the form y = mx + c.

  1. 1Gradient of k = 12
  2. 2y − 10 = 12(x − 3)
  3. 3y = 12x − 26

Answery = 12x − 26

Part (d) · 4 marks

Find where k meets the x-axis at C, then find the exact area of triangle ABC.

  1. 1At C, y = 0: 12x − 26 = 0 → x = 13/6
  2. 2Base BC = 123 − 13/6 = 725/6, height = 10 (y-coordinate of A)
  3. 3Area = ½ × 10 × 725/6 = 3625/6

Answer3625/6

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