Rotation and Enlargement
A rotation turns a shape about a centre by an angle, and an enlargement changes its size by a scale factor from a centre.
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Play with the controls to see the idea in action.
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A rotation turns a shape about a centre by an angle, and an enlargement changes its size by a scale factor from a centre.
- Rotations need a centre, angle and direction
- Enlargements need a centre and scale factor
- Enlargements keep shape but change size
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Rotation and Enlargement?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Rotation and Enlargement. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Rotation and Enlargement in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Rotation and Enlargement gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Rotation and Enlargement in detail
A rotation turns a shape about a fixed point through an angle in a given direction, such as 90° clockwise about (1, 2). To describe one fully, you must state the centre, angle and direction. The image is congruent to the original.
An enlargement changes size by a scale factor from a centre of enlargement: each distance from the centre is multiplied by the scale factor. A factor greater than 1 makes it bigger, between 0 and 1 makes it smaller and a negative factor flips it to the other side of the centre. Enlargements give similar shapes and are used in maps, models and photography.
How the interactive helps you understand Rotation and Enlargement
Watch the shape transformation in the interactive. Use any sliders or buttons it offers to change the values and see how the shape transformation responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Rotation and Enlargement.
Real-life uses and examples
- Spot Rotation and Enlargement in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Rotation and Enlargement by estimating first, then working it out step by step.
- Use Rotation and Enlargement when comparing prices, discounts or recipe quantities in everyday life.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Rotation and Enlargement.
- Memorising the steps for Rotation and Enlargement without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Rotation and Enlargement
What is Rotation and Enlargement?
A rotation turns a shape about a centre by an angle, and an enlargement changes its size by a scale factor from a centre.
What are the most important points about Rotation and Enlargement?
The main points are: Rotations need a centre, angle and direction; Enlargements need a centre and scale factor; Enlargements keep shape but change size.
Why is Rotation and Enlargement useful?
Understanding Rotation and Enlargement gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Rotation and Enlargement?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Rotation and Enlargement?
Related topics in Mathematics include Probability Basics, Relative Frequency, Quartiles and Box Plots.