Rotations (Edexcel GCSE Maths): Revision Notes
Rotations
What is a rotation?
A rotation is a transformation that turns a shape around a fixed point. When we rotate a shape, it moves in a circular path around this fixed point, but the shape itself doesn't change size.
To fully describe any rotation, you must provide three essential pieces of information:
- The centre of rotation - the fixed point around which the shape turns
- The angle of rotation - how far the shape turns (measured in degrees)
- The direction of rotation - whether the shape turns clockwise or anticlockwise
Centre of rotation
The centre of rotation is the fixed point that the shape rotates around. This point stays in exactly the same position during the rotation.
Often, the centre of rotation is the origin (0, 0) on a coordinate grid. However, the centre can be any point, and when it's not the origin, you'll be given the coordinates of this point.
Angle of rotation
The angle of rotation tells us how far the shape has turned. This is always measured in degrees, not as fractions of turns.
The most common rotation angles you'll encounter are:
- 90° - this is a quarter turn
- 180° - this is a half turn
Exam tip: Always give angles in degrees. Don't write "quarter turn" or "half turn" in your answer - write "90°" or "180°".
Direction of rotation
The direction of rotation describes which way the shape turns:
- Clockwise - turning in the same direction as clock hands
- Anticlockwise - turning in the opposite direction to clock hands
Special case: When rotating by 180°, you don't need to specify the direction. This is because a 180° clockwise rotation gives exactly the same result as a 180° anticlockwise rotation.
Properties of rotated shapes
When you rotate a shape, the rotated shape is congruent to the original shape. This means:
- The rotated shape is exactly the same size
- The rotated shape is exactly the same shape
- Only the position and orientation have changed
How to perform rotations
The most reliable method for rotating shapes uses tracing paper:
- Mark the centre of rotation with a cross (×)
- Trace the original shape onto tracing paper
- Place your pencil or compass point on the centre of rotation
- Rotate the tracing paper by the required angle in the correct direction
- Mark the new position of the rotated shape
This tracing paper method helps you rotate shapes accurately and check your answers. It's particularly useful in exams where precision is important.
Worked example walkthrough
Worked Example: Rotating a shape 180° about point (0, 1)
Let's look at rotating a shape 180° about the point (0, 1):
- First, mark the centre of rotation (0, 1) with a cross
- Trace the original shape
- Place your pencil on the centre point (0, 1)
- Rotate the tracing paper 180°
- Mark where the shape appears in its new position
Since this is a 180° rotation, we don't need to specify clockwise or anticlockwise direction.
Describing rotations in exams
When describing a rotation in an exam, you must write the word "rotation" and then give:
- The angle of the turn (in degrees)
- The direction of the turn (clockwise or anticlockwise, unless it's 180°)
- The centre of rotation (as coordinates if it's not the origin)
Example answer format: "Rotation 90° clockwise about the point (2, 1)"
Make sure your answer follows this exact format to get full marks.
Key Points to Remember:
- Always include all three elements: centre, angle, and direction (except for 180° rotations)
- Use degrees, not fractions: write "90°" not "quarter turn"
- Rotated shapes are congruent to the original shape
- Tracing paper is your best tool for accurate rotations
- Mark the centre with a cross before you start rotating