Lemmara logoLemmaraWorked solution

WMA11/01 Oct 2024, Question 1: Equation of a Line Through Two Points

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks

The question, in short

Line l₁ goes through A(−5, 20) and B(3, −4). Find l₁ in y = mx + c form, then find the perpendicular line l₂ through the midpoint of AB in px + qy + r = 0 form.

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

Part (a) · 3 marks

Find the equation of l₁ through A(−5, 20) and B(3, −4), giving it as y = mx + c.

  1. 1Gradient = (20 − (−4))/(−5 − 3) = 24/(−8) = −3
  2. 2y + 4 = −3(x − 3)
  3. 3y = −3x + 5

Answery = −3x + 5

Part (b) · 3 marks

Find the equation of l₂, perpendicular to l₁ through the midpoint of AB, in the form px + qy + r = 0 with integer coefficients.

  1. 1Midpoint of AB = ((−5 + 3)/2, (20 − 4)/2) = (−1, 8)
  2. 2Perpendicular gradient = 1/3
  3. 3y − 8 = (1/3)(x + 1), so 3y − 24 = x + 1
  4. 4x − 3y + 25 = 0

Answerx − 3y + 25 = 0

Stuck on a step? Read the free lesson: Equation of a Line Through Two Points

Practise more equation of a line through two points 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 of a line through two points

Also searched as: WMA11 October 2024 · WMA11/01 · wma11 oct24 · IAS Maths Pure Mathematics 1 October 2024 · question 1.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.