Transformations
Reflection, rotation, translation and enlargement — and describing them fully.
Review these first
Learning objectives
What you need to be able to do
Teacher-mapped phrasing — check against the official Cambridge syllabus for exact wording.
- 7.1.1Carry out and fully describe reflections, rotations, translations and enlargements.
6 minute read
Transformations
Marks here are awarded for complete descriptions. Each transformation has a required set of details, and missing one loses the mark.
The four transformations and what a full description needs
- Reflection — name the transformation and give the equation of the mirror line (e.g.
y = x,x = 2). - Rotation — give the angle, the direction (clockwise or anticlockwise), and the centre of rotation. All three are required.
- Translation — give the column vector
(x above y), where the top number is movement right and the bottom is movement up (negatives for left and down). - Enlargement — give the scale factor and the centre of enlargement.
One transformation only
If asked to "describe the transformation", give exactly one. Writing "reflection then translation" scores zero even if it is geometrically true — the question guarantees a single transformation exists.
Enlargement details
- A scale factor between 0 and 1 makes the image smaller, though it is still called an enlargement.
- A negative scale factor puts the image on the opposite side of the centre, inverted.
- Only enlargement changes size; reflection, rotation and translation are congruent transformations, preserving lengths and angles.
Finding a centre
For a rotation or enlargement, join corresponding points of object and image; the lines meet at the centre. For rotation, use perpendicular bisectors of the joins instead.
Think of it like this
A full description is a set of directions precise enough for someone else to reproduce the move exactly. "Rotate it" is as useless as "go that way" — the angle, direction and pivot are what make it repeatable.
Worked examples
Method, step by step
A triangle is mapped onto an identical triangle turned upside down, with the point (2, 3) fixed. Describe the transformation fully.
- 1The image is the same size, so it is not an enlargement.
- 2It is inverted but not mirrored in a line through the shape, suggesting a rotation of 180°.
- 3The fixed point is the centre of rotation.
- 4At 180°, clockwise and anticlockwise are identical, so direction need not be specified.
A rotation of 180° about the centre (2, 3).
Common misconceptions
- Describing a rotation without the centre, or without the direction. All three details are required.
- Thinking a scale factor of ½ is a "reduction" and not an enlargement. The term covers any scale factor.
- Giving two transformations when one is asked for, which scores nothing.
In the exam
- Learn the required details as a checklist: reflection → mirror line; rotation → angle, direction, centre; translation → vector; enlargement → scale factor, centre.
- Check whether the image is the same size. If it is, the transformation cannot be an enlargement.