Which transformation has been applied to shape A to get shape B?
Shape moves without changing orientation.
The shape has been translated (slid across).
Transformations
Transformations describe how shapes move or change through translation, reflection, rotation and enlargement. They link closely to coordinates, similarity and graph transformations.
Overview
A transformation changes the position, size or orientation of a shape.
The original shape is called the object, and the new shape is called the image.
In GCSE Maths, you need to recognise and describe four main transformations: translation, reflection, rotation and enlargement.
You should be able to recognise each transformation from a diagram and describe it using correct mathematical language.
What you should understand after this topic
- Recognise each transformation from a diagram or description
- Describe transformations fully using correct exam language
- Use coordinate rules for reflections and rotations
- Find centres of rotation and enlargement
- Avoid common GCSE transformation mistakes
Key Definitions
Transformation
A change to a shape’s position, size or orientation.
Object
The original shape before a transformation.
Image
The new shape after a transformation.
Translation
A movement of a shape without changing size or orientation.
Reflection
A flip of a shape in a mirror line.
Rotation
A turn of a shape around a fixed point.
Enlargement
A change in size using a scale factor.
Scale Factor
The number that determines how much a shape is enlarged or reduced.
Centre of Rotation
The point around which a shape rotates.
Centre of Enlargement
The point from which a shape is enlarged.
Key Rules
Translation
Describe using a vector.
Reflection
Describe using the mirror line.
Rotation
Give the angle, direction and centre.
Enlargement
Give the scale factor and centre.
Quick Recognition
Same size + moved
Translation
Same size + flipped
Reflection
Same size + turned
Rotation
Different size
Enlargement
Describe Fully Checklist
Translation
Give the vector only.
Reflection
Give the exact mirror line.
Rotation
Give the angle, direction and centre.
Enlargement
Give the scale factor and centre.
How to Solve
Step 1: Understand transformations
A transformation maps an object to an image. It can move, flip, turn or resize a shape.
Object = original shape.
Image = transformed shape.
Exam tip: Always describe the transformation fully.
Step 2: Know the four transformations
Translation
Moves a shape using a vector.
Reflection
Flips a shape in a mirror line.
Rotation
Turns a shape around a centre.
Enlargement
Changes size using a scale factor.
Step 3: Translation
Every point moves the same distance and direction.
Move across first, then up/down.
Write as a vector.
Answer format: \(\begin{pmatrix}x \\ y\end{pmatrix}\)
Step 4: Reflection
A reflection flips a shape across a mirror line.
Give the equation of the mirror line.
Points stay the same distance from the line.
Step 5: Rotation
A rotation turns a shape around a centre.
State angle (90°, 180°, 270°).
State direction (clockwise/anticlockwise).
State centre of rotation.
Step 6: Enlargement
An enlargement changes size from a centre.
State the scale factor.
State the centre.
Scale factor > 1 → bigger, < 1 → smaller
Step 7: Describe transformations fully
Translation
Vector
Reflection
Mirror line
Rotation
Angle, direction, centre
Enlargement
Scale factor, centre
Step 8: Exam method summary
See graph transformations for functions.
- Compare object and image.
- Identify the transformation.
- Find key detail (vector, line, centre, scale).
- Use correct mathematical language.
- Check another point.
Example Questions
Edexcel
Exam-style questions inspired by Edexcel GCSE Mathematics.
Edexcel
Describe fully the single transformation that maps shape A onto shape B.
Edexcel
Shape A is reflected in the x-axis and then translated by the vector \( \begin{pmatrix} c \\ d \end{pmatrix} \).
Find the value of c and the value of d.
Edexcel
Reflect the shaded shape in the mirror line.
Edexcel
Here are two triangles on a grid. Triangle B is an enlargement of triangle A.
Write down the scale factor of the enlargement.
AQA
Exam-style questions based on the AQA GCSE Mathematics specification, focusing on clear reasoning, accurate diagram interpretation, and precise mathematical communication.
AQA
Work out the vector that translates shape A to shape B.
AQA
Rectangle A can be mapped onto rectangle B by a single transformation.
A student claims that the transformation is a reflection in the y-axis.
Is the student correct?
Tick one box. Yes ☐ No ☐
Give a reason for your answer.
AQA
Here are two triangles, P and Q.
A student makes the following statement:
The transformation that maps triangle \(P\) onto triangle \(Q\) is a reflection in the line \(x = -1\).
Make one criticism of the student's statement.
AQA
Here is triangle ABC on a coordinate grid.
Describe a single transformation that maps the triangle so that:
\(B\) remains fixed,
\(A\) maps to \((1, 1)\),
\(C\) maps to \((1, -1)\).
OCR
Exam-style questions aligned with OCR GCSE Mathematics, emphasising logical reasoning, problem-solving skills, and precise use of mathematical terminology.
OCR
Triangle A and triangle B are drawn on a coordinate grid.
(a) Complete the following transformations of triangle A.
\(\text{(i) Draw the image of triangle } A \text{ after a rotation of } 180^{\circ} \text{ about } (0,0).\)
\(\text{(ii) Draw the image of triangle } A \text{ after a translation by the vector } \begin{pmatrix} 2 \\ -7 \end{pmatrix}.\)
\(\text{(b) Describe fully the single transformation that maps triangle } A \text{ onto triangle } B.\)
OCR
(a) Draw the image of triangle A after a reflection in the line \( y = -1 \).
(b) Describe fully the single transformation that maps triangle A onto triangle B.
OCR
Exam Checklist
Step 1
Check whether the shape stayed the same size.
Step 2
Ask: did it move, flip, turn or resize?
Step 3
Track one point first, then confirm with another.
Step 4
Give every detail needed for full marks.
Most common exam mistakes
Rotation
Missing the centre or forgetting clockwise / anticlockwise.
Reflection
Giving the wrong mirror line or measuring distance incorrectly.
Translation
Writing the vector in the wrong direction.
Enlargement
Forgetting the scale factor or using the wrong centre.
Common Mistakes
These are common mistakes students make when working with transformations in GCSE Maths.
Missing rotation direction
Incorrect
A student gives the angle but not the direction.
Correct
Always state both the angle and the direction (clockwise or anticlockwise) for rotations.
Not stating the centre of rotation
Incorrect
A student describes the rotation without a centre.
Correct
Every rotation must include the centre of rotation as coordinates.
Incomplete “describe fully” answers
Incorrect
A student gives only part of the required information.
Correct
Include all details: rotation (angle, direction, centre), reflection (mirror line), translation (vector), enlargement (scale factor and centre).
Incorrect translation vector
Incorrect
A student gives the wrong direction or order.
Correct
Write vectors as \(\begin{pmatrix} x \\ y \end{pmatrix}\), where x is horizontal and y is vertical movement.
Incorrect reflection measurement
Incorrect
A student measures diagonally instead of perpendicular to the mirror line.
Correct
Reflection distances must be measured at right angles to the mirror line.
Describing enlargement vaguely
Incorrect
A student says “bigger” or “smaller”.
Correct
Always give the exact scale factor (e.g. scale factor 2 or 0.5).
Wrong centre of enlargement
Incorrect
A student uses an incorrect centre point.
Correct
Draw lines from corresponding points to find the correct centre of enlargement.
Misunderstanding negative scale factors
Incorrect
A student places the image on the same side.
Correct
A negative scale factor places the image on the opposite side of the centre of enlargement.
Try It Yourself
Practise performing and describing geometric transformations.
Foundation
Foundation Practice
Recognise and apply translations, reflections, rotations and enlargements.
Translate the point (2, 3) by vector (4, -1). Write the new coordinates.
Add to x and y separately.
(2 + 4, 3 − 1) = (6, 2).
Which transformation flips a shape over a line?
Think mirror.
A reflection flips a shape over a line.
Reflect the point (3, 2) in the y-axis. What are the new coordinates?
Change the sign of x.
Reflection in y-axis → (-3, 2).
Which transformation changes the size of a shape?
Think scaling.
Enlargement changes the size of a shape.
A shape is enlarged by scale factor 2. A side was 3 cm. Find the new length.
Multiply by scale factor.
3 × 2 = 6 cm.
Which transformation turns a shape around a point?
Think spinning.
A rotation turns a shape around a point.
Rotate the point (2, 1) 180° about the origin. What are the new coordinates?
Both signs change.
(2, 1) → (-2, -1).
Reflect the point (4, -3) in the x-axis.
Change the sign of y.
(4, -3) → (4, 3).
A shape is translated 3 right and 2 up. Write the vector.
Right = positive x, up = positive y.
Vector = (3, 2).
Higher
Higher Practice
Describe transformations fully, including vectors, centres and scale factors.
Describe the translation from A to B.
Count horizontal and vertical movement.
Moved 3 right and 2 up → (3, 2).
Which transformation maps shape A onto B?
Check mirror symmetry.
It is a reflection in the y-axis.
A shape is enlarged by scale factor 3 from centre (0,0). A point is (2,1). Find its image.
Multiply coordinates.
(2 × 3, 1 × 3) = (6, 3).
Which transformation keeps size but changes orientation?
Think turning.
Rotation keeps size but changes orientation.
Rotate (3, 2) 90° anticlockwise about the origin.
(x, y) → (-y, x).
(3, 2) → (-2, 3).
A shape is enlarged with scale factor 1. What happens?
Multiply by 1.
Scale factor 1 means no change.
Reflect (−5, 2) in the y-axis.
Change x sign.
(-5, 2) → (5, 2).
Which transformation preserves distances and angles?
Think rigid transformations.
Translations, rotations and reflections preserve shape and size.
Rotate (4, −1) 180° about the origin.
Both signs change.
(4, −1) → (−4, 1).
A shape is enlarged by scale factor 0.5. What happens?
Scale factor less than 1 shrinks.
The shape is reduced in size.
Games
Practise performing and describing geometric transformations.
Choose a game to begin.
Frequently Asked Questions
What are the 4 transformations?
Translation, reflection, rotation and enlargement.
What does 'describe fully' mean?
Include all key details such as direction, angle, centre or scale factor.
Which transformations keep size?
Translation, reflection and rotation.