## Transformations

The four transformations; reflectionrotation, translation and enlargement are studied in more detail in Year 9 and Year 11.

Below is a summary of each:

### Reflection

When a shape or point is reflected its image is on the opposite side of a mirror line or axis of symmetry.

The mirror line is halfway between the shape and its image.

The axis of symmetry is often shown by the letter m.

The object and the image are congruent, the same shape and size.

Length, angle size and shape are said to be invariant for reflection, which means they do not change.

Examples of reflections −  The diagram shows a reflection in the mirror line m

### Rotation

rotation is a transformation where a point, or an object, is turned around a fixed point to a new position called the image.

The object and the image are the same shape and the same size but in different positions.

When a shape or point is rotated there is a centre of rotation which remains fixed.

The angle of rotation gives the number of degrees that the shape is rotated through.

An anti-clockwise rotation is said to bepositive.

A clockwise rotation is said to be negative.

Examples of rotations −  The diagram shows an anti-clockwise quarter turn rotation about the centre of rotation, O.

### Translation

A translation is a transformation where all points move the same distance and in the same direction.

The object and the image are the same shape and thesame size.

Translations can be represented by vectors.

In general the vector can represent a translation where x is the horizontal movement and y is the vertical movement.

Examples of translations −  The diagram shows a translation of ### Enlargement An enlargement is a transformation where the size of an object changes.

Examples of enlargements − The object becomes larger or smaller.

If points on the object and the corresponding points on the image are joined with a straight line, these straight lines meet at the centre of enlargement.

The scale factor for an enlargement tells how much an object has been enlarged by.

negative scale factor means the object and the image are on opposite sides of the centre of enlargement. The diagram shows an enlargement, centre O with a scale factor of 2.

 An interactive spreadsheet of reflections, rotations, translations and enlargements. (Excel) A explanation about Transformations (Powerpoint). A worksheet on Reflection (Word). A worksheet on Rotation (Word). 