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Maths · KS3 and GCSE · Interactive lesson

Transformations: slide, reflect, turn and resize

Follow a shape on a coordinate grid. Compare an original with its image and describe a translation, reflection, rotation or enlargement.

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Explore an interactive example, then try the questions at your own pace.

Lesson options

Start with the idea, then use the method when you are ready. Changing these settings changes the example. Your current practice question is kept.

Start with the idea explains the basics. Use the method builds on them with more detail.

KS3 / GCSE. These examples use translations, axis reflections, quarter turns and positive whole-number enlargements. Fractional and negative scale factors are not included.

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KS3 / GCSE · start with the idea

By the end of this lesson: Describe and follow one transformation on a coordinate grid.

The interactive diagram and controls are in Stage 2, “Explore one example”. Read the idea here, then try it next.

The idea in small steps
  • A translation slides every point the same distance in the same direction.
  • Add the horizontal movement to x. Add the vertical movement to y.
  • Right and up are positive; left and down are negative. The shape keeps its size.
What do the words mean?
Coordinates (x, y)
The horizontal position x followed by the vertical position y.
Origin
The point (0, 0), where the axes cross.
Image
The shape after a transformation.
Scale factor
The number multiplying each distance from the centre of enlargement.

Change the example

Something to try

Set the horizontal move to zero. Change only the vertical move. Which coordinate changes?

Notice what changes

Move 3 units right and 2 units down. Original and image triangles on a coordinate grid.Purple: original · orange: image-6-6-4-4-2-2224466xy0A (1, 1) → A′ (4, -1)
A (1, 1) → A′ (4, -1)
About this model

The dashed purple triangle is the original. Orange is its image; dots mark the matching A points. Coordinates count across, then up; one grid square is one unit. Reflection lines and all centres used here are stated explicitly.

The example you chose
Move 3 units right and 2 units down. Original and image triangles on a coordinate grid.Purple: original · orange: image-6-6-4-4-2-2224466xy0A (1, 1) → A′ (4, -1)

A (1, 1) → A′ (4, -1)

Still picture of the example from Stage 2. Use the back arrow to change it.

Work through it

Starting example: read the steps below

  1. Start with A (1, 1), B (3, 1) and C (1, 3).
  2. Move 3 units right and 2 units down.
  3. Change x: 1 + 3 = 4.
  4. Change y: 1 − 2 = -1.
  5. The image has A′ (4, -1), B′ (6, -1), C′ (4, 1).

Try on your own

Your turn. No rush.

Question 1

Point A is (-2, 0). Move 7 units right and 1 unit up. What is the x-coordinate of its image?

Enter a number or fraction, such as −3, 0.75 or 3/4. You can include the matching unit shown above. If rounding is needed, the question tells you how many decimal places to use.

About these questions

Questions appear in a mixed order. Work at your own pace and stop whenever you like.

These questions use their own numbers, separate from the lesson example. You can stop whenever you like. Answers last for this visit to the page.

A good place to pause

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Can you describe the transformation precisely and check a matching point?

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Notes for parents and tutors

These lessons cover selected KS3 and GCSE ideas for England; they are not a complete course. The level notes explain where GCSE methods or optional extensions begin. Maurice can help you choose material for your course and exam board.

The content draws on the DfE Maths curriculum, DfE Science curriculum and AQA GCSE Physics specification. Level labels are guidance, not exam-board endorsements. For AQA Radioactivity, calculating net decline as a ratio is Higher-tier work. Net means the overall change; ask Maurice whether this extension is relevant to your course. Explanations and practice were reviewed during development on 21 October 2026; Maurice should check their fit before assigning work.

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