4MA1/1F Jun 2022, Question 25: Length of a Line Segment
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 4 marks
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The question, in short
Two circles on a cm grid: C₁ centre (−1, 3) radius 13 cm, C₂ centre (7, 18) radius 6 cm. Find the centre-to-centre distance and justify why the circles intersect.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 3 marks
Calculate the distance between the centres (−1, 3) and (7, 18).
- 1Change in x: 7 − (−1) = 8; change in y: 18 − 3 = 15
- 2Distance = √(8² + 15²) = √(64 + 225) = √289
- 3Distance = 17
Answer17
Part (b) · 1 mark
Explain why C₁ and C₂ intersect, using the radii and the distance found.
- 113 + 6 = 19
- 219 > 17
- 3The sum of the radii is greater than the distance between the centres
- 4So the circles intersect
Answer13 + 6 > 17
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