Midpoint
Find the midpoint of A(−4, −1) and B(2, 5).
- Add the x-coordinates and halve: (−4 + 2) ÷ 2 = −1
- Add the y-coordinates and halve: (−1 + 5) ÷ 2 = 2
Answer: (−1, 2)
Midpoint & length of a line segment
Coordinate Rescue Mission
Mapped to Cambridge IGCSE 0580 E3.4 (length and midpoint) and GCSE A8 and G20, with question types taken from recent papers: “find the coordinates of the midpoint of AB”, “the length of AB is k√5, find k”, “AP : PB = 1 : 3”, and the perpendicular bisector.
Length and midpoint of a line segment are IGCSE Extended only (0580 E3.4).
What students practise
- The midpoint of a line segment, from a grid and from coordinates
- Missing endpoints, unknown coordinates and the end of a diameter
- Length with Pythagoras, whole-number and to 3 significant figures
- Exact lengths as surds in simplest form; “the length is k√5” (Higher)
- Unknown coordinates from a length: two answers (Higher)
- Dividing a line in a ratio and extending a line with vectors (Higher)
- Exam problems: isosceles triangles, perimeters, radius from a diameter, the perpendicular bisector
How it works
Learn
12 lessons, each labelled with the exams it is for, with an interactive model and worked examples.
Practise
Six stations, six fresh questions each visit, with hints that fade.
Challenge
Mixed questions from every station with a skill-by-skill report.
For teachers
Open Teacher Options in the game to choose skills and levels. Nothing is uploaded: progress stays in each student's browser, so no accounts or data-protection paperwork are needed.
Which exams it covers
Midpoint and length of a line segment appear in both GCSE tiers. In Cambridge IGCSE 0580 they are Extended content only.
| Topic | GCSE (AQA, Edexcel) | Cambridge IGCSE 0580 |
|---|---|---|
| Reading and plotting coordinates | A8 | C3.1 / E3.1 |
| Midpoint of a line segment | G11 | E3.4 (Extended only) |
| Length of a line segment (Pythagoras) | G11, G20 | E3.4 (Extended only) |
| Missing endpoint from a midpoint | G11 | E3.4 (Extended only) |
| Length as a surd in its simplest form | G20, N8 (Higher) | E3.4, E1.18 (Extended) |
| Dividing a line in a ratio; extending a line with vectors | R4, G25 (Higher) | E7.2 / E7.4 (Extended: position vectors and ratio) |
| Perpendicular bisector of a segment | A9 (Higher) | E3.4 + E3.7 (Extended) |
Worked examples
Four examples of the question types in the game.
Length of a line segment
Find the distance between (1, 2) and (7, 10).
- Horizontal change: 7 − 1 = 6
- Vertical change: 10 − 2 = 8
- Distance = √(6² + 8²) = √100
Answer: 10 units
Missing endpoint
M(3, −1) is the midpoint of AB, and A is (−2, 4). Find B.
- From A to M: x goes up by 5, y goes down by 5
- Do the same again from M: x = 3 + 5 = 8, y = −1 − 5 = −6
Answer: B(8, −6)
Ratio · Higher
P divides AB in the ratio 1 : 2, with A(1, 2) and B(10, 14). Find P.
- 1 : 2 means P is 1/3 of the way from A to B
- From A to B: x changes by 9, y changes by 12
- P = (1 + 9 ÷ 3, 2 + 12 ÷ 3)
Answer: P(4, 6)
Common mistakes the game targets
- Subtracting in the midpoint formula. The midpoint is the average: add the coordinates, then halve.
- Losing negative signs when squaring. (−3)² = 9, so a negative change still adds to the length.
- Averaging M and A to find a missing endpoint. That gives a point between them. Go the same step again past M instead.
- Reading 1 : 2 as halfway. A ratio of 1 : 2 splits the segment into 3 parts, so P is 1/3 of the way along.
- Leaving a surd unsimplified. √52 is the right value but not the simplest form: the game asks for 2√13, as the mark scheme does.
- Finding only one value. When a length is given and a coordinate is unknown, the square root gives ±, so there are usually two answers.
Questions teachers and parents ask
Is the game free?
Yes. It is free to use, with no account, no adverts and no tracking.
Which exams does it suit?
GCSE Foundation and Higher (AQA and Edexcel), and Cambridge IGCSE 0580 Extended. Midpoint and length are not on the IGCSE Core syllabus. Every lesson shows which exam and tier it is for.
Can I change the level?
Yes. Teacher options switch between Foundation and Higher / Extended. Higher adds exact surd lengths, dividing a line in a ratio and the perpendicular bisector.
Are exact answers accepted?
Yes. Distances can be given as simplified surds such as 2√13, or as decimals rounded as the question asks.
Are the questions like real exam questions?
Yes. They follow recent IGCSE 0580 and GCSE papers, for example “the length of AB is k√5, find k”, “find the y-coordinate of the midpoint of A(a, 12) and B(b, 27)”, and the 2025 kite question on the diagonals BD : AC = 2 : 3.
Need worksheets and lessons to go with the games?
Printable IGCSE and GCSE resources from Mathwright: worksheets, exam-style practice and full worked solutions.
More coordinate geometry games
Coordinates & the four quadrants
Coordinate Treasure Map
Travel from Base Camp to the Treasure Chest by reading, plotting and moving between coordinates in all four quadrants.
Gradient & straight-line graphs
Gradient City
Six stations covering every straight-line question on IGCSE and GCSE papers: gradient, drawing graphs, y = mx + c, parallel and perpendicular lines, and real-life gradients.
Translations, reflections, rotations & enlargements
Transformation Station
Draw the image on the grid and describe fully the single transformation, exactly as on IGCSE 0580 and GCSE papers.