The Four Transformations

Definition of Transformation: A transformation in mathematics is a process by which a set of points, called ‘the object’, is moved to a new position, creating ‘an image’.

Translation

A translation is a slide, moving a shape a specific distance in a specific direction.
It keeps the same size and shape. The positions change, but the distances between points and angles between lines remain the same.
Translations are described using vectors. The top number in the vector indicates movement left (-) or right (+) and the bottom number shows the movement down (-) or up (+).

Reflection

Reflection is when a shape is flipped over a line, giving a mirror image.
The shape stays the same size and keeps its original shape. The position changes, but distances and angles stay the same.
The line of reflection is the ‘mirror line’.

Rotation

Rotation is when a shape is turned around a fixed point.
The original shape retains its size and shape but its position and orientation change.
A rotation is described by the centre of rotation, the angle of rotation, and the direction (clockwise or anti-clockwise).

Enlargement

Enlargement involves a shape being scaled up or down, affecting the size but not the shape.
The position may change, but the shape remains similar. Angles stay the same, but lengths change in proportion.
An enlargement is described by its scale factor and centre of enlargement. If the scale factor is greater than 1, the shape enlarges. If it’s less than 1 (but not zero), the shape reduces.

Transformation Properties

All transformations preserve the shape of an object.
Translations, reflections and rotations preserve the size of an shape.
The only transformation that can change the size of an object is enlargement.

Application of The Transformations

To answer transformation questions, apply each transformation separately and in order.
Make sure to follow exact instructions when translating, reflecting, rotating or enlarging shapes.
When reflecting and rotating, use tracing paper to ensure accuracy.
When enlarging, use a ruler to measure lengths accurately and ensure you maintain the correct ratio.

Stay Mindful

Misinterpreting scale factors and directions are common mistakes. Pay close attention to these details.
Skipping a step in a series of transformations can lead to incorrect solutions.
Practise transformation problems frequently to increase speed and accuracy. Don’t rely on visual estimation, always use the right tools.

Final Note

Revision and practice are key to mastering transformations. Try to understand the concepts and then apply them in different contexts to improve your grasp on the topic.