A transformation changes the position, orientation or size of a shape while following specific rules. Common transformations include reflection, rotation, translation and enlargement. Understanding how to describe and draw these accurately is essential in geometry.

 

 

Reflection in a Given Line

A reflection is a flip of a shape across a straight line called the mirror line.

 

Key properties of reflection:
• the mirror line is the same distance from corresponding points
• corresponding points lie on a line perpendicular to the mirror line
• the shape is reversed but remains the same size

 

To draw a reflection:
• draw the mirror line clearly
• measure the perpendicular distance from each point to the line
• plot each reflected point the same distance on the opposite side
• join the reflected points in the same order

 

The mirror line does not move during a reflection

 

 

Rotation

A rotation turns a shape around a fixed point called the centre of rotation.

 

In this topic, rotations are:
• \( 90^\circ \) clockwise
• \( 90^\circ \) anticlockwise
• \( 180^\circ \)

 

The size and shape do not change during a rotation.

 

To draw a rotation:
• mark the centre of rotation
• draw lines from the centre to key points of the shape
• rotate each point by the given angle in the correct direction
• keep the distance from the centre the same

 

A \( 180^\circ \) rotation produces the same result clockwise or anticlockwise.

 

Always check the direction of rotation

 

 

Translation

A translation slides a shape without turning or resizing it.

 

The shape keeps:
• the same size
• the same orientation

 

A translation is described using horizontal and vertical movement.

 

To draw a translation:
• move every point the same distance
• move right or left for horizontal movement
• move up or down for vertical movement

 

For example, a translation may be described as:
• 4 units right and 2 units up

 

Each point must move exactly the same amount.

 

 

Enlargement

An enlargement changes the size of a shape using a scale factor and a centre of enlargement.

 

In this topic, the scale factor is:
• a positive integer
• or a positive fraction

 

Key properties of enlargement:
• angles stay the same
• sides change in length
• the shape stays similar

 

To draw an enlargement:
• mark the centre of enlargement
• draw straight lines from the centre through each point
• multiply the distance from the centre by the scale factor
• plot the new points and join them

 

If the scale factor is greater than 1, the shape gets larger.
If the scale factor is between 0 and 1, the shape gets smaller.

 

The centre of enlargement stays fixed

 

 

Describing Transformations

When describing a transformation, always include the correct information.

 

For reflection:
• the line of reflection

 

For rotation:
• the angle
• the direction
• the centre of rotation

 

For translation:
• the horizontal movement
• the vertical movement

 

For enlargement:
• the scale factor
• the centre of enlargement

 

Incomplete descriptions lose marks.

 

 

Key Points to Remember

Reflections flip shapes across a mirror line.
Rotations turn shapes about a centre by a given angle and direction.
Translations slide shapes without changing orientation.
Enlargements change size using a scale factor and a centre.
Accurate drawing depends on careful measurement and clear diagrams.

 

Being confident with transformations allows shapes to be moved, resized and described precisely in geometric problems.