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WMA11/01 Oct 2021, Question 5: Perpendiculars: Feet and Areas

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 8 marks

The question, in short

Line l₁ is 3y − 2x = 30; l₂ passes through A(24, 0) and is perpendicular to l₁, meeting it at P. Find P algebraically, then the area of triangle BPA where l₁ meets the x-axis at B.

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

Part (a) · 5 marks

Find the coordinates of P, where l₁ and l₂ intersect, using algebra and showing working.

  1. 1l₁: y = (2/3)x + 10, gradient 2/3
  2. 2l₂ gradient = −3/2: y = −3/2(x − 24), i.e. 2y + 3x = 72
  3. 3Solve: (2/3)x + 10 = −3/2(x − 24)
  4. 4Multiply by 6: 4x + 60 = −9x + 216, so 13x = 156, x = 12
  5. 5y = (2/3)(12) + 10 = 18, so P = (12, 18)

AnswerP(12, 18)

Part (b) · 3 marks

Given l₁ crosses the x-axis at B, find the area of triangle BPA.

  1. 1B: y = 0 in 3y − 2x = 30 gives x = −15
  2. 2Base BA = 24 − (−15) = 39, height = 18
  3. 3Area = ½ × 39 × 18 = 351

Answer351

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