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Transformations (Mathematics Lesson)

What Are Transformations?

In geometry, a transformation is a process of changing the position, orientation and/or size of a shape.

There are 4 types of transformations:

Types of Transformations

Translation (or Slide)

A translation moves a shape without rotating, reflecting or resizing it.

It is as if the shape has been slid to a new position without turning it or resizing it.

Each point on the shape moves the same direction and distance.



The diagram above shows a triangle before (light blue) and after (dark blue) being translated.

The triangle has been moved, but has not been rotated, reflected nor resized. Each point on the triangle has been moved by the same direction and distance (shown by the arrow).

Read more about translations

Reflection (or Flip)

A reflection transforms a shape so that it becomes a mirror image of itself.

The shape is reflected in a line called the line of reflection.

It is as if the shape has been flipped.

Each point in the image (the reflection) is the same perpendicular distance from the line of reflection as the corresponding point in the object. The image is the same size as the object.



The diagram above shows a triangle before (light blue) and after (dark blue) being reflected.

The triangle has been reflected in the y-axis. Each point on the reflected triangle is the same perpendicular distance from the mirror line as the corresponding point on the object. The reflected shape is the same size.

Read more about reflections

Rotation (or Turn)

A rotation turns a shape around a center.

It is as if the shape has been turned.

Each point in the rotated shape is the same distance from the center as the original shape. The image is the same size as the object.



The diagram above shows a triangle before (light blue) and after (dark blue) being rotated.

Each point on the rotated triangle is the same distance from center (marked with a red cross) the corresponding point on the original shape. The rotated shape is the same size.

Read more about rotations

Enlargement

An enlargement makes the shape larger (or smaller).



The diagram above shows a triangle before (light blue) and after (dark blue) being enlarged.

The shape has been enlarged about a center of enlargement (marked with a red cross).

The enlarged shape is twice as large as the original shape. The length of the line drawn from the center of enlargement to each point on the enlarged triangle is twice the length of the line drawn from the center to the corresponding point on the original shape.

Read more about enlargements
Curriculum
Geometry Lessons
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Note

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 or any of translation, reflection and rotation, then the two shapes are similar.

Similar shapes are identical in shape but not in size.

All the shapes below are similar: