Lemmara logoLemmaraWorked solution

WMA11/01 Jun 2025, Question 5: Equation in the Form ax + by + c = 0

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 7 marks

The question, in short

Find the perpendicular line through the origin, its intersection with x − 2y + 25 = 0, then the shortest distance from that line to the origin as a simplified surd.

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

Part (a) · 2 marks

Find the equation of the line through the origin perpendicular to x − 2y + 25 = 0.

  1. 1l₁: y = ½x + 25/2, so its gradient is ½
  2. 2Perpendicular gradient = −2
  3. 3l₂ passes through the origin: y = −2x

Answery = −2x

Part (b) · 3 marks

Use algebra to find the coordinates where the two lines meet.

  1. 1Substitute y = −2x into x − 2y + 25 = 0
  2. 2x + 4x + 25 = 0, so x = −5
  3. 3y = −2(−5) = 10, so P is (−5, 10)

AnswerP(−5, 10)

Part (c) · 2 marks

Hence work out the shortest distance from the origin to the line x − 2y + 25 = 0, simplified surd.

  1. 1Shortest distance = OP
  2. 2OP = √((−5)² + 10²) = √125
  3. 3= 5√5

Answer5√5

Stuck on a step? Read the free lesson: Equation in the Form ax + by + c = 0

Practise more equation in the form ax + by + c = 0 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 equation in the form ax + by + c = 0

Also searched as: WMA11 June 2025 · WMA11/01 · wma11 jun25 · IAS Maths Pure Mathematics 1 June 2025 · question 5.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.