Lemmara logoLemmaraWorked solution

4PM1/02 Jun 2019, Question 8: Length of a Line Segment

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 11 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Given points A(2, 6), B(6, 8) and C(4, 2), work out side lengths, angles of triangle ABC, then the centre and radius of its circumcircle.

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

Part (a) · 4 marks

Calculate the exact lengths of AB, BC and AC using the coordinates of the three points.

  1. 1AB² = 4² + 2² = 20 → AB = √20 = 2√5
  2. 2BC² = 2² + 6² = 40 → BC = √40 = 2√10
  3. 3AC² = 2² + 4² = 20 → AC = √20 = 2√5

Answer(i) AB = √20 (ii) BC = √40 (iii) AC = √20

Part (b) · 3 marks

Determine the size in degrees of each of the three angles of triangle ABC.

  1. 1AB² + AC² = 20 + 20 = 40 = BC², so ∠A = 90°
  2. 2AB = AC so the triangle is isosceles
  3. 3∠B = ∠C = 45°

Answer∠A = 90°, ∠B = 45°, ∠C = 45°

Part (c) · 2 marks

Find the coordinates of P, the centre of the circle through A, B and C.

  1. 1∠A = 90°, so BC is a diameter
  2. 2P = midpoint of BC = ((6 + 4)/2, (8 + 2)/2) = (5, 5)

AnswerP(5, 5)

Part (d) · 2 marks

Work out the exact radius of the circle, giving it in the form √a with integer a.

  1. 1Radius = ½ × BC
  2. 2= ½√40 = √10

Answer√10

Stuck on a step? Read the free lesson: Length of a Line Segment

Practise more length of a line segment 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 length of a line segment

Also searched as: 4PM1 2 June 2019 · 4PM1/02 · 4pm1 jun19 2 · question 8.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.