0580
Transformations
Vectors and Transformations
Object, image and what changes
- The starting shape is the object and the result is the image, with the image's vertices labelled A′, B′, C′ to match A, B, C
- Three of the four keep the shape exactly the same size, so object and image are congruent: reflection, rotation and translation
- Only enlargement changes the size, and even then the shape stays similar
- A point that does not move under a transformation is invariant
- A ruler must be used for every straight edge, which the syllabus states directly
Exam tip
"Describe fully" appears in 24 of the 43 papers, and it means one transformation and every one of its parameters. Two transformations described where one was asked for scores nothing, however correct both are. The schemes also reject "turn", "shift", "spin" and "rot" — only the proper name earns the mark.
What each transformation needs
| Transformation | What a question can ask for |
|---|---|
| Reflection | a mirror line that is any straight line, including y = x and y = −x |
| Rotation | any centre, through a multiple of 90° |
| Enlargement | positive, fractional and negative scale factors |
| Translation | a column vector |
| Combinations | two transformations one after the other, described as a single one |