Lemmara logoLemmaraWorked solution

4PM1/01 Jun 2020, Question 5: Perpendicular Lines

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Given points P(4, 7), Q(3, 0), R(10, 1) and S(11, 8), work with lines PR and QS and the quadrilateral PQRS.

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

Part (a) · 3 marks

Use calculation to show that lines PR and QS are perpendicular.

  1. 1Gradient PR = (7 − 1)/(4 − 10) = −1
  2. 2Gradient QS = (8 − 0)/(11 − 3) = 1
  3. 3(−1) × 1 = −1, so PR ⊥ QS

AnswerGradient PR = −1, gradient QS = 1, product = −1 so PR and QS are perpendicular

Part (b) · 2 marks

Find the exact lengths of (i) PR and (ii) QS.

  1. 1PR = √(6² + 6²) = √72 = 6√2
  2. 2QS = √(8² + 8²) = √128 = 8√2

AnswerPR = 6√2, QS = 8√2

Part (c) · 2 marks

Find the area of quadrilateral PQRS.

  1. 1The diagonals PR and QS are perpendicular
  2. 2Area = ½ × PR × QS = ½ × 6√2 × 8√2
  3. 3= 48

Answer48

Stuck on a step? Read the free lesson: Perpendicular Lines

Practise more perpendicular lines questions

Real 4PM1 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 perpendicular lines

Also searched as: 4PM1 1 June 2020 · 4PM1/01 · 4pm1 jun20 1 · question 5.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.