Describing and Drawing Two Successive Transformations
⭐ Higher Tier Content
Two successive transformations means one transformation is carried out and then a second transformation is carried out on the result. The order matters because doing the same two transformations in a different order can give a different final image.
What Successive Transformations Are
A transformation maps an object to an image.
With two successive transformations:
• the first transformation maps the object to an intermediate image
• the second transformation maps the intermediate image to the final image
When describing them, you must state both transformations clearly.
Always apply the first transformation before the second
How to Draw Two Successive Transformations
To draw two successive transformations accurately:
Draw the original shape and label it clearly.
Carry out the first transformation and draw the intermediate image.
Label the intermediate image clearly so it is not confused with the final image.
Carry out the second transformation on the intermediate image.
Label the final image clearly.
Using different labels such as object, image 1 and image 2 helps keep the steps clear.
Describing Successive Transformations
A complete description must include the details of both transformations.
For reflection:
• the line of reflection
For rotation:
• the angle
• clockwise or anticlockwise
• the centre of rotation
For translation:
• the horizontal movement
• the vertical movement
For enlargement:
• the scale factor
• the centre of enlargement
A correct description should state them in order.
Example description style:
First reflect the shape in the line shown.
Then translate the image 4 units right and 2 units up.
This clearly describes the two steps.
Order Matters
Successive transformations do not always commute.
For example, reflecting then translating may give a different result from translating then reflecting.
This is why the problem statement and the order you apply must be followed carefully.
Common Errors to Avoid
Common mistakes include:
• performing the second transformation on the original shape instead of the intermediate image
• missing information such as the line of reflection or the centre of rotation
• mixing up clockwise and anticlockwise
• describing the transformations in the wrong order
Working step by step reduces these errors.
Key Points to Remember
Two successive transformations are done one after the other.
The first transformation produces an intermediate image.
The second transformation is applied to the intermediate image.
Descriptions must include full details for both transformations.
The order of transformations can change the final result.
Understanding successive transformations helps you analyse combined movements and describe them clearly and accurately on diagrams.