Transformations
Rotations
A rotation turns a shape around a fixed point called the centre of rotation. In this chapter we turn shapes 90° — a quarter turn — clockwise or anticlockwise.
Turning about a centre
A rotation turns a whole shape around one fixed point, the centre of rotation. Every part of the shape turns through the same angle. In this chapter the angle is always 90°, which is a quarter turn.
Clockwise and anticlockwise
Clockwise means turning the same way as the hands of a clock. Anticlockwise means turning the opposite way. A 90° clockwise turn and a 90° anticlockwise turn move the shape in opposite directions.
Using tracing paper
To rotate a shape: trace it, put your pencil point on the centre of rotation, turn the tracing paper 90° (a quarter turn) in the direction you want, then draw the new shape and label it.
What stays the same
A rotation only turns the shape — it does not change its size or shape. Matching corners before and after the turn are called corresponding vertices.
Worked examples
Rotating 90° clockwise about a centre
- Trace the shape and put your pencil point on the centre of rotation.
- Turn the tracing paper 90° (a quarter turn) clockwise.
- Draw the shape in its new position and label it.
Answer: The shape has been turned a quarter turn clockwise about the centre.
Rotating 90° anticlockwise
- Keep your pencil point on the centre of rotation.
- This time turn the tracing paper 90° anticlockwise — the opposite way.
- Draw the new shape.
Answer: The shape has been turned a quarter turn anticlockwise about the centre.
Clockwise or anticlockwise?
- Facing North, a 90° clockwise turn goes towards East.
- Facing North, a 90° anticlockwise turn goes towards West.
- The two turns go in opposite directions.
Answer: Clockwise and anticlockwise are opposite turning directions.
The size does not change
- Compare the shape before and after rotating.
- Every length is the same; only the direction it faces has changed.
Answer: A rotated shape is exactly the same size and shape as the original.
Where you see this in real life
- Designing rubber play-park flooring by turning, reflecting and translating shapes.
- Turning through a quarter turn when you change the direction you face.
- A camera on a tripod turning to point at a new subject.
Key words
- Rotation
- A turn of a shape around a fixed point.
- Centre of rotation
- The fixed point that a shape turns around.
- Clockwise
- Turning the same way as the hands of a clock.
- Anticlockwise
- Turning the opposite way to the hands of a clock.
- Quarter turn
- A turn of 90°.