What is Rotation?
A rotation is a type of geometric transformation where a shape is turned around a fixed point. Think of it like a wheel spinning around its axle, or the hands of a clock turning around the centre.
A transformation that turns a figure about a fixed point called the centre of rotation, through a specified angle and in a specified direction (clockwise or anticlockwise).
Every rotation is described by three pieces of information:
- Centre of rotation — the fixed point around which the shape turns
- Angle of rotation — how far the shape turns (measured in degrees)
- Direction of rotation — clockwise (CW) or anticlockwise (ACW / counterclockwise)
Imagine placing your finger on a point on a piece of paper, then spinning the paper around your finger. Your finger is the centre of rotation, the amount you spin is the angle, and which way you spin is the direction.
Describing Rotations
When describing a rotation, you must always state all three pieces of information:
- Centre of rotation — given as a coordinate, e.g. or
- Angle of rotation — e.g. , , , or any other angle
- Direction — clockwise or anticlockwise
A rotation of is the same whether you go clockwise or anticlockwise — so for you don't need to specify a direction, though it's good practice to include it.
Common rotation angles you'll encounter:
- — a quarter turn
- — a half turn
- — a three-quarter turn
- — a full turn (the shape returns to its original position)
A clockwise rotation is the same as a anticlockwise rotation. Similarly, a clockwise rotation is the same as a anticlockwise rotation. This can help you check your work!
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