Lemmara logoLemmaraWorked solution

WMA11/01 Jan 2020, Question 6: Parallel Lines and Their Equations

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

The question, in short

Line l₁ is 3x − 4y + 20 = 0; l₂ passes through R(8, 0) and is parallel to l₁. Find l₂'s equation, then use parallelogram PQRS with l₁ meeting the axes at P and Q to find its area and point S.

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

Part (a) · 3 marks

Find the equation of l₂ in the form ax + by + c = 0 with integer coefficients.

  1. 1Rearrange l₁: y = (3/4)x + 5, so the gradient is 3/4
  2. 2l₂ through (8, 0): y = (3/4)(x − 8)
  3. 34y = 3x − 24, so 3x − 4y − 24 = 0

Answer3x − 4y − 24 = 0

Part (b) · 3 marks

Given PQRS is a parallelogram, calculate the area of PQRS.

  1. 1P: y = 0 gives x = −20/3, so P(−20/3, 0); Q: x = 0 gives y = 5, so Q(0, 5)
  2. 2PR = 8 + 20/3 = 44/3 is the base on the x-axis; the height is OQ = 5
  3. 3Area = 44/3 × 5 = 220/3

Answer220/3 (≈ 73.3)

Part (c) · 2 marks

Find the coordinates of vertex S of the parallelogram.

  1. 1In PQRS, S = P + (R − Q)
  2. 2R − Q = (8, −5)
  3. 3S = (−20/3 + 8, 0 − 5) = (4/3, −5)

AnswerS(4/3, −5)

Stuck on a step? Read the free lesson: Parallel Lines and Their Equations

Practise more parallel lines and their equations questions

Real XMA01 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on parallel lines and their equations

Also searched as: WMA11 January 2020 · WMA11/01 · wma11 jan20 · IAS Maths Pure Mathematics 1 January 2020 · question 6.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.