Rotations
Turn a figure around a point by an angle.
Key idea
Turn a figure around a point by an angle.
In depth
A rotation turns a shape around a fixed centre by a given angle and direction. Distances to the centre stay the same. A 90° anticlockwise rotation about the origin sends (x, y) to (−y, x).
Worked example
(3, 1) rotated 90° anticlockwise about the origin → (−1, 3).
Real-world uses
- Turning a gear or a wheel
- Rotating a 3D model on screen
- Clock hands moving through angles
Common mistake
Rotating clockwise when anticlockwise is requested.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Rotations?
Turn a figure around a point by an angle. It is a topic at the intermediate level in Geometry.
Where is Rotations used in real life?
Real-world examples: Turning a gear or a wheel; Rotating a 3D model on screen; Clock hands moving through angles.
What should I learn before Rotations?
Make sure you are comfortable with Reflections, the previous topic in Geometry.
What is a common mistake with Rotations?
Rotating clockwise when anticlockwise is requested.
How can I practise Rotations?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Rotations?
Move on to Dilations next.
Related intermediate topics in Geometry
- Vertical Angles – Opposite angles formed by intersecting lines are equal.
- Parallel Lines and Transversals – Corresponding and alternate interior angles are equal.
- Exterior Angle Theorem – An exterior angle equals the sum of the two remote interior angles.
- Triangle Inequality – Any two sides sum to more than the third.
- Congruent Triangles – Same shape and size: SSS, SAS, ASA, AAS, HL.
- Similar Triangles – Same shape, proportional sides: AA, SAS~, SSS~.