GCSE Maths • Foundation & Higher
GCSE Transformations Revision Guide
Move, turn, flip and resize shapes accurately on coordinate grids.
Foundation
Exam practice
Worked examples
What You'll Learn
Translate Shapes
Read and write column vectors and move every vertex consistently.
Reflect Shapes
Use repeated faces or compact formulae without omissions.
Rotate Shapes
Use the correct centre, angle and clockwise or anticlockwise direction.
Enlarge Shapes
Apply positive, fractional and negative scale factors from a centre.
Transform Coordinates
Use coordinate rules when the axis, origin or centre makes them appropriate.
Describe Transformations Fully
State every feature required to identify a unique transformation.
Key Rules and Formulas
Surface Area Lessons
Enlargement
Use centres and positive, fractional or negative scale factors.
Reflection
Construct mirror images and describe the line of reflection.
Rotation
Rotate accurately using a centre, angle and direction.
Translation
Move points and shapes using column vectors.
CORE SUBTOPICS
Object and Image
The original is the object; the transformed result is the image, often labelled with primes.
Column Vectors
Write horizontal movement above vertical movement in a two-entry column.
Lines of Reflection
Use equations such as x=2, y=−3 or y=x and equal perpendicular distances.
Centres of Rotation
Corresponding points remain the same distance from the centre.
Centres of Enlargement
Lines through pairs of corresponding vertices meet at the centre.
Invariants
Recognise which properties stay unchanged under each transformation.
Worked Example
Enlargement from a Centre
QUESTION
Triangle ABC has vertices A(2,2), B(4,2) and C(2,5). Enlarge it by scale factor −2 about the centre O(1,1). Find A′, B′ and C′.
- Given information: For each vertex P, use P′=O+k(P−O), where k=−2.
- Method: Find the displacement from O, multiply both components by −2, then add O back.
- A−O=(1,1). Multiply by −2 to get (−2,−2), so A′=(−1,−1).
- B−O=(3,1). Multiply by −2 to get (−6,−2), so B′=(−5,−1).
- C−O=(1,4). Multiply by −2 to get (−2,−8), so C′=(−1,−7).
- Plot A′, B′ and C′ and join them in the same corresponding order.
- Check: OA′, OB′ and OC′ are twice the corresponding original distances and lie on opposite rays from O.
- Final answer: A′(−1,−1), B′(−5,−1), C′(−1,−7).
- Independent answer check: AB=2 and A′B′=4; AC=3 and A′C′=6, confirming length scale factor |−2|=2.
- One common mistake: Do not multiply the original coordinates by −2 unless the centre of enlargement is the origin.
- Common GCSE Mistakes
- Giving an Incomplete Description
- Mixing Vector Order
- Reversing Signs
- Reflecting in the Wrong Line
- Rotating about the Origin Automatically
- Confusing Clockwise and Anticlockwise
- Ignoring the Centre of Enlargement
- Treating a Reduction as Division by Coordinates
- Use the centre-to-vertex displacement and the given scale factor.
- Misreading Negative Scale Factors
- Joining Vertices in the Wrong Order
- Exam Tips
- Label corresponding vertices before transforming a whole shape.
- Transform each vertex separately, then join the image in the same order.
- Use tracing paper if permitted for rotations and check equal distance from the centre.
- For reflections, draw or highlight the mirror line before counting squares.
- Write translation vectors as horizontal movement over vertical movement.
- When identifying an enlargement centre, extend lines through at least two corresponding vertex pairs.
- Check whether the image should be congruent or similar to the object.
Ready to Practice?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Transformations Tutorial
Clear, step-by-step explanation of expanding brackets, simplifying complex expressions, and solving for x. Perfect for visual learners who need a breakdown of the rules in action.
- 12 minute comprehensive guide
- High-definition whiteboard walk-through
Continue Your GCSE Maths Revision
Continue Your GCSE Maths Revision
Frequently Asked Questions
Translation, reflection, rotation and enlargement.
Translations, reflections and rotations preserve length, angle and area, so object and image are congruent.
Give the angle, clockwise or anticlockwise direction, and centre of rotation.
Give the scale factor and centre of enlargement.
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