"Fully describe the single transformation" is one of the most common GCSE instructions — and one of the easiest to lose marks on. Each transformation requires specific pieces of information, and missing any one of them means lost marks.
What Are the Four Transformations?
The four transformations at GCSE are reflection, rotation, translation, and enlargement. Each moves or resizes a shape in a specific way, and the exam expects you to identify which transformation has been applied and then describe it completely.
A fully described transformation must include all the required details. Simply writing "rotation" or "reflection" without the additional information will score zero or one mark out of the available marks.
At Higher tier you may also be asked about combined transformations — where two transformations are applied in sequence and you describe the single equivalent transformation.
It is essential to practise identifying each type quickly, as the exam typically gives you the original and image shapes and asks you to "fully describe" the transformation in words.
Key Formulas
Step-by-Step Method
- Identify the transformation type by comparing the original shape and its image (same size and orientation? reflected? rotated? bigger or smaller?).
- Add the required details — see the checklist below for each type.
- Write a complete sentence including the transformation name and all required information.
What you need for each transformation:
- Reflection: the equation of the mirror line (e.g., x = 2 or y = x).
- Rotation: the angle, the direction (clockwise or anticlockwise), and the centre of rotation.
- Translation: the column vector.
- Enlargement: the scale factor and the centre of enlargement.
Worked Example 1 — Foundation Level
Question: Shape A is mapped to Shape B by a reflection. Shape A has vertices at (1, 2), (1, 5), (3, 5). Shape B has vertices at (5, 2), (5, 5), (3, 5). Fully describe the transformation.
Working: The shapes are mirror images. The midpoint of (1, 2) and (5, 2) is (3, 2). The midpoint of (1, 5) and (5, 5) is (3, 5). The mirror line passes through x = 3.
Answer: Reflection in the line x = 3.
Worked Example 2 — Higher Level
Question: Triangle P has vertices at (2, 1), (4, 1), (4, 3). Triangle Q has vertices at (−1, 2), (−1, 4), (−3, 4). Fully describe the single transformation that maps P to Q.
Working: The triangle has been rotated. The orientation has changed and the shape is congruent. Testing 90° anticlockwise about the origin: (2, 1) → (−1, 2), (4, 1) → (−1, 4), (4, 3) → (−3, 4). All points match.
Answer: Rotation, 90° anticlockwise, centre (0, 0).
Worked Example 3 — Exam Style
Question: Shape A has vertices at (1, 1), (3, 1), (3, 2). Shape B has vertices at (4, 4), (10, 4), (10, 7). Fully describe the single transformation.
Working: The shape has changed size. Scale factor = 6 ÷ 2 = 3 (using the base lengths). To find the centre, draw lines through corresponding vertices. The line from (1, 1) to (4, 4) extends back to (−0.5, −0.5)... Using the formula: centre = ((3×1 − 4)/(3−1), (3×1 − 4)/(3−1)) = (−0.5, −0.5).
Answer: Enlargement, scale factor 3, centre (−0.5, −0.5).
Common Mistakes
- Not naming the transformation. You must state "reflection," "rotation," "translation," or "enlargement" — this is usually worth one mark on its own.
- Missing the mirror line equation for reflections. Writing "reflected" without the line equation (e.g., y = −1 or x = 3) is incomplete.
- Forgetting the direction for rotations. You must state clockwise or anticlockwise (unless the angle is 180°, where direction is irrelevant).
- Giving coordinates instead of a column vector for translations. A translation must be described with a column vector, not as a set of coordinates.
- Not finding the centre for enlargements. The centre of enlargement is essential — draw ray lines through corresponding vertices to locate it.
Exam Tips
- Count the details needed: reflection needs 2 (name + line), rotation needs 4 (name + angle + direction + centre), translation needs 2 (name + vector), enlargement needs 3 (name + scale factor + centre).
- A negative scale factor (Higher) means the image is on the opposite side of the centre and inverted.
- Fractional scale factors (e.g., ½) produce a smaller image — still called an "enlargement."
- For combined transformations, apply each transformation in order, then describe the net effect as a single transformation.
Practice Questions
Q1 (Foundation): Shape A is translated so that point (2, 3) moves to (5, 1). Write down the column vector of the translation.
Q2 (Foundation): Shape P is reflected in the y-axis. Describe what happens to the point (4, 7).
Q3 (Higher): Triangle A is mapped to Triangle B by a rotation of 180° about the point (1, 2). Point (3, 5) is a vertex of A. Find the corresponding vertex of B.
Practise describing transformations questions with instant feedback — completely free on GCSEMathsAI.
Related Topics
- Transformations – Reflection, Rotation, Translation
- Transformations – Enlargement and Scale Factor
- Congruence and Similarity
Summary
- There are four transformations: reflection, rotation, translation, and enlargement.
- Each requires specific details to be "fully described" — missing any detail loses marks.
- Reflection: name + mirror line equation. Rotation: name + angle + direction + centre. Translation: name + column vector. Enlargement: name + scale factor + centre.
- At Higher tier, scale factors can be negative or fractional, and combined transformations may be tested.
- Always start by identifying whether the shape has changed size, orientation, or both.
- Reflection, rotation, and translation produce congruent shapes; enlargement produces similar shapes.
- Invariant points (points that do not move) can help identify centres of rotation and mirror lines.
Test your understanding
5 quick MCQs to identify any misconceptions on this topic.
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