Rotations
Maths: Edexcel IGCSE Higher, topic 5.2.2
Describing Transformations
Transformation can be used to describe how a shape or point moves on coordinate axes.
Object and image
- The original shape or point before a transformation is known as the object.
- The new shape or point after a transformation is known as the image.
Describing a rotation
- An angle of rotation and a centre of rotation are required to describe a rotation.
- The angle of rotation tells you how much the object rotates by.
- You can often tell the angle of rotation by comparing the orientation (way round) of the object and image.
- The centre of rotation tells you where the rotation centres around.
Angle of rotation
- Look at the orientation to work out the angle of rotation.
Centre of rotation
- Find the centre of rotation using tracing paper.
- Draw around the object and place your pencil where you think the centre of rotation is.
Centre of rotation cont.
- Use trial and error until you rotate the object on the tracing paper and it makes the image.
- This takes a lot of practice to get good at but it gets easier the more you try it.
Rotations
Using x and y coordinates, we can rotate shapes on a graph.
90o rotation
- Shape A has rotated 90o anti-clockwise to become shape B, with its centre of rotation at the origin.
- The x and y coordinates for shape A and B swapped.
- The x coordinates have changed sign but the y coordinates have not.
180o rotation
- Shape A has rotated 180o anti-clockwise to become shape B, with its centre of rotation at the origin.
- The x and y coordinates for shape A and B are the same but have changed sign.
270o rotation
- Shape A has rotated 270o clockwise to become shape B, with its centre of rotation at the origin.
- The x and y coordinates for shape A and B swapped.
- The y coordinates have changed sign but the x coordinates have not.
Clockwise and Anti-clockwise
- A positive angle of rotation is defined as the angle of rotation in an anti-clockwise direction
- A negative angle of rotation is defined as the angle of rotation in a clockwise direction.
Test yourself on Rotations
What information do you need to complete a rotation?
How many degrees has shape A rotated to become shape B?
How many degrees has shape A rotated to become shape B?
How many degrees clockwise has shape A rotated to become shape B?
How many degrees has shape A rotated to become shape B?