IGCSE Math RevisionQuestion 1
Find the midpoint of the line segment joining \((2, 7)\) and \((8, -1)\).
Show the worked answer
- Mean of the \(x\)-coordinates: \(\frac{2 + 8}{2} = 5\). Mean of the \(y\)-coordinates: \(\frac{7 + (-1)}{2} = 3\).
Answer: \((5, 3)\)
Cambridge IGCSE Maths (0580) · Topic 3: Coordinate geometry · 3.4
Cambridge IGCSE Maths 0580 Length and Midpoint of a Line Segment Questions
Length and Midpoint of a Line Segment questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
- 9 questions
- 9 Extended
- 7 non-calculator
- Free, no sign-in
What the syllabus asks
- 3.4 Length and midpoint Extended only
Extended: The length of a line segment and the coordinates of its midpoint from its end points.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Length and Midpoint of a Line Segment questions: Extended
Extended content, for Papers 2 and 4.
Question 2
Calculate the distance between the points \((-2, 1)\) and \((10, 6)\).
Show the worked answer
- Across \(12\), up \(5\).
- Length \(= \sqrt{12^2 + 5^2} = \sqrt{169} = 13\).
Answer: \(13\)
Question 3
Find the length of the line joining \((1, 2)\) and \((7, 10)\).
Show the answer and mark scheme
- M1 6² + 8² or √(36 + 64)
- A1 10
Answer: \(10\)
Question 4
Find the length of the line segment joining \((-3, 4)\) and \((2, -1)\). Give your answer correct to 3 significant figures.
Show the worked answer
- Across \(5\), down \(5\).
- Length \(= \sqrt{5^2 + 5^2} = \sqrt{50} = 7.071\ldots\)
Answer: \(7.07\)
Question 5
\(M(4, 1)\) is the midpoint of \(AB\). \(A\) is \((-2, 5)\).
Find the coordinates of \(B\).
Show the worked answer
- From \(A\) to \(M\): \(x\) goes up \(6\), \(y\) goes down \(4\).
- Do the same again from \(M\): \(B = (4 + 6, 1 - 4)\).
Answer: \(B(10, -3)\)
Question 6
\(M(2, -1)\) is the midpoint of the line \(AB\). \(A\) is the point \((-3, 4)\). Find the coordinates of \(B\).
Show the answer and mark scheme
- M1 2 × 2 − (−3) or 2 × (−1) − 4, or a correct step from A to M repeated
- A1 (7, −6)
Answer: \((7, -6)\)
Question 7
\(A(1, 3)\) and \(B(7, 11)\) are the ends of a diameter of a circle.
Find the centre and the radius of the circle.
Show the worked answer
- Centre \(=\) midpoint of \(AB = \left(\frac{1 + 7}{2}, \frac{3 + 11}{2}\right) = (4, 7)\).
- \(AB = \sqrt{6^2 + 8^2} = 10\), so the radius is \(5\).
Answer: Centre \((4, 7)\), radius \(5\)
Question 8
\(P\) is \((k, 2)\) and \(Q\) is \((5, 6)\). The length of \(PQ\) is \(5\).
Find the two possible values of \(k\).
Show the worked answer
- \((5 - k)^2 + (6 - 2)^2 = 25\), so \((5 - k)^2 = 9\).
- \(5 - k = 3\) or \(5 - k = -3\).
Answer: \(k = 2\) or \(k = 8\)
Question 9
The vertices of a triangle are \(A(-2, 1)\), \(B(4, 3)\) and \(C(1, -4)\). Calculate the perimeter of the triangle. Give your answer correct to 3 significant figures.
Show the answer and mark scheme
- M1 one of AB = √40, BC = √58, CA = √34
- M1 all three lengths
- M1 adds their three lengths
- A1 19.8 (19.77…)
Answer: \(19.8\)
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Keep going
- Coordinate geometry practice for 0580: more questions, each one marked, tagged Core or Extended
- My mistakes, then a Skill Builder on the skills you missed
- Common mistakes in 0580: what the Cambridge examiner reports say
- Coordinate geometry revision notes and the 0580 formula sheet
- Cambridge IGCSE Maths 0580 past papers, when you are ready for a full paper
Questions students ask
Which Cambridge 0580 papers can test length and midpoint of a line segment?
Length and Midpoint of a Line Segment is Extended content (syllabus 3.4), so it is tested only on the Extended papers, Paper 2 (non-calculator) and Paper 4 (calculator). Core candidates do not need it.
Are these Cambridge past-paper questions?
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
Where can I practise more length and midpoint of a line segment questions?
In the 0580 practice for topic 3 (Coordinate geometry), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.