The Lesson
A transformation is a change of a shape.
A transformation can change a shape's position, orientation and its size.
Types of Transformations
There are 4 types of transformations:
Translation (or Slide)
A translation moves a shape.
A translation is a slide of a shape (without rotating, reflecting or resizing it).
The diagram below shows a triangle before (light blue) and after (dark blue) being translated:
Each point on the shape moves the same direction and distance (shown by the arrow).
Read more about translations
Reflection (or Flip)
A reflection makes a shape a mirror image of itself.
A reflection flips a shape in a line (called the line of reflection).
The diagram below shows a triangle before (light blue) and after (dark blue) being reflected:
Each point in the image (the reflection) is the same perpendicular distance from the line of reflection (in this case, the
yaxis) as the corresponding point in the object.
Read more about reflections
Rotation (or Turn)
A rotation turns a shape.
A rotation turns a shape around a point (called the centre of rotation).
The diagram below shows a triangle before (light blue) and after (dark blue) being rotated:
Each point on the rotated triangle is the same distance from centre of rotation as the corresponding point on the original shape.
Read more about rotations
Enlargement
An enlargement makes a shape larger (or smaller).
An enlargement resizes a shape about a point (called the centre of enlargement).
The diagram below shows a triangle before (light blue) and after (dark blue) being enlarged:
The enlarged shape is twice as large as the original shape. The length of the line drawn from the centre of enlargement to each point on the enlarged triangle is twice the length of the line drawn from the centre to the corresponding point on the original shape.
Read more about enlargements
Images and Objects

The original shape before the transformation is called an object.

The shape after it has been transformed is called the image.
Congruent Shapes
If a shape can be transformed to another using only translation, reflection and rotation, then the two shapes are
congruent.
Congruent shapes have the same size, line lengths, angles and areas.
All the shapes below are congruent:
Similar Shapes
If a shape can be transformed to another using enlargement, then the two shapes are
similar.
Similar shapes are identical in shape but not in size.
All the shapes below are similar: