MathematicsExam code: 0580
Transformations
Vectors and Transformations
The Four 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
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 |