Translation
Translate the point A(−5, 8) by the vector 4−2.
- Top number: move 4 right, so x = −5 + 4 = −1
- Bottom number: move 2 down, so y = 8 − 2 = 6
Answer: A′(−1, 6)
Translations, reflections, rotations & enlargements
Transformation Station
Transformations appear on 38 of the 63 recent Cambridge IGCSE 0580 papers we checked. Students draw images by tapping the grid and answer “describe fully” questions detail by detail, with feedback that works like the mark scheme.
📘 Revision guide: How to describe a transformation fully
What students practise
- Translations by column vectors, and the vector back
- Reflections in x = a and y = b (Core), y = x and y = −x (Extended)
- Rotations of 90° and 180° about the origin or a vertex (Core) or any centre (Extended)
- Enlargements with positive and fractional scale factors, and negative scale factors (Extended)
- Describing a transformation fully: every detail that earns a mark
- Combined transformations as a single transformation (Extended / Higher)
- Mapping back and invariant points (GCSE Higher)
How it works
Learn
12 lessons, each labelled with its IGCSE 0580 and GCSE references, with interactive rotation and enlargement models.
Practise
Six stations: draw the image on the grid, or describe it fully with mark-by-mark feedback.
Challenge
Mixed questions from every station with a skill-by-skill report.
For teachers
Open Teacher options to choose Core / Foundation (the IGCSE Core limits) or Extended / Higher. Nothing is uploaded: progress stays in each student's browser, so no accounts or data-protection paperwork are needed.
Which exams it covers
All four transformations are Foundation and Core content. Negative scale factors and combined transformations are Higher and Extended.
| Topic | GCSE (AQA, Edexcel) | Cambridge IGCSE 0580 |
|---|---|---|
| Translation by a column vector | G7, G24 | C7.1 / E7.1 |
| Reflection in a line | G7 | C7.1 (vertical and horizontal lines) / E7.1 |
| Rotation about a centre | G7 | C7.1 (multiples of 90°) / E7.1 |
| Enlargement: positive and fractional scale factors | G7 | C7.1 / E7.1 |
| Enlargement: negative scale factors | G7 (Higher) | E7.1 (Extended only) |
| Combined transformations | G8 (Higher) | E7.1 (Extended only) |
| Invariant points | G8 (Higher) | Not named on 0580 |
Worked examples
Four examples of the question types in the game.
Rotation
Rotate (3, 1) through 90° clockwise about the origin.
- The rule for 90° clockwise about the origin is (x, y) → (y, −x)
- (3, 1) → (1, −3)
Answer: (1, −3)
Enlargement
Enlarge the point (3, 2) by scale factor 2, centre (1, 1).
- Vector from the centre to the point: 21
- Double it: 42
- Add to the centre: (1 + 4, 1 + 2)
Answer: (5, 3)
Combined transformations · Higher
Reflect in the x-axis, then in the y-axis. Which single transformation does the same?
- x-axis: (x, y) → (x, −y)
- then y-axis: (x, −y) → (−x, −y)
- (x, y) → (−x, −y) is a half turn about the origin
Answer: rotation of 180° about (0, 0)
Common mistakes the game targets
- Describing a transformation without all the details. Rotation needs angle, direction and centre; enlargement needs scale factor and centre; reflection needs the equation of the line.
- Mixing up the vector's numbers. The top number moves left or right, the bottom number moves up or down.
- Turning the wrong way. Clockwise and anticlockwise give different images unless the angle is 180°.
- Enlarging from the origin instead of the centre. Measure every distance from the centre of enlargement.
- Negative scale factors on the same side. A negative scale factor puts the image on the opposite side of the centre, upside down.
- Confusing y = x with y = −x. Reflecting in y = x swaps the coordinates; in y = −x it swaps them and changes both signs.
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?
Cambridge IGCSE 0580 Core and Extended (C/E7.1), and GCSE Foundation and Higher (G7, G8, G24). Every lesson shows its references.
How do students draw the image?
They tap the grid to mark each corner of the image (or type the coordinates). The correct image is shown if they get it wrong.
How is “describe fully” marked?
Students choose the transformation and give each detail. The feedback ticks each detail separately, like the mark scheme.
Can I keep to IGCSE Core?
Yes. Teacher options set Core / Foundation: vertical and horizontal mirror lines, centres at the origin or a vertex, positive scale factors and no combined transformations.
Matching worksheet packs
Printable practice and exam-style tests on the same topic, with full worked solutions.
Geometry, trigonometry & vectors
Vectors — IGCSE 0580 Paper 2
Paper 2 (non-calculator) style practice and an exam-style test.
Free practice: Transformation Station
Geometry, trigonometry & vectors
Vectors — IGCSE 0580 Paper 4
Paper 4 (calculator) style practice and an exam-style test.
Free practice: Transformation Station
Need worksheets and lessons to go with the games?
Printable IGCSE and GCSE resources from Mathwright: worksheets, exam-style practice and full worked solutions.
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