Geometry (Mathematics Curriculum)

Transformations

What Is a Transformation?

A transformation is a change of a shape. A transformation can change a shape's position, orientation and its size.

There are four types of transformations: translation, rotation, reflection and enlargement (or in simpler language: slide, turn, flip and resize).

Here are some examples from transformations. We might be interested in sliding (translating) a shape. We might want to turn (rotate) a shape. We might want to flip (reflect) a shape in a line. We might want to resize (enlarge) a shape. Transformations allow us to do this.

The Curriculum

The lessons are grouped into mini-curriculum to help you organise your learning.

A brief description is given for each mini-curriculum. Click the MORE button to learn more.

Transformations

A transformation is a change in a shape so that its angles and proportions are kept the same, but it has been slided, turned, flipped or resized.

In this mini-curriculum, you will learn the basics of transformations.

Transformations

A transformation is a change of a shape. A transformation can change a shape's position, orientation and its size.

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Translation

A translation moves a shape without flipping, turning or resizing it.

In this mini-curriculum, you will learn about translation.

Translation

A translation moves a shape. A translation is a slide of a shape: without rotating, reflecting or resizing it.

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

Translate a Shape

To translate a shape, break the translation down into:

  • how far we move the shape in a horizontal direction (left or right).

  • how far we move the shape in a vertical direction (up or down).

Use a column vector to describe how far to move the shape in these directions.

Describe a Translation

To describe a translation:

  • find how far a shape has moved in a horizontal direction (left or right).

  • find how far a shape has moved in a vertical direction (up or down).

Write these in a column vector.

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Rotation

A rotation turns a shape. It changes a shape's orientation.

In this mini-curriculum, you will learn about rotation.

Rotation

A rotation turns a shape. It is a turn of a shape about a point (called the center of rotation).

All points move in a circle around the center of rotation, so that each point stays the same distance from the center of rotation.

Common Rotations

Common rotations are rotations of 90°, 180°, 270° and 360° about the origin.

Rotate a Shape

To rotate a shape, rotate each point on the shape by the same angle about a center of rotation.

Describe a Rotation

To describe a rotation, find the center of rotation and the angle that each point rotates about it.

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Reflections

A reflection flips a shape. It is as if a shape looks in a mirror.

In this mini-curriculum, you will learn about reflection.

Reflection

A reflection flips a shape. It is is a flip of a shape about a line (called the line of reflection).

Each point on the shape is the same perpendicular distance from the line of reflection as the corresponding point on the reflected shape.

Common Reflections

Common reflections are reflections in the x-axis (y = 0), the y-axis (x = 0), the line x = c, the line y = c, the line y = x and the line y = −x.

Reflect a Shape

To reflect a shape, draw the line of reflection. Draw each point on the reflected shape the same perpendicular distance from the line of reflection as the corresponding point on the original shape.

Describe a Reflection

To describe a rotation, find the line of reflection.

Join corresponding points on the shape and its reflection with a line. The line of reflection passes throught the midpoint if these lines.

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Enlargements

An enlargement resizes a shape. It makes a shape larger or smaller.

In this mini-curriculum, you will learn about enlargements.

Enlargement

An enlargement resizes a shape. It makes a shape larger or smaller.

All sides of the shape get larger or smaller by the same amount, so that the lengths of the sides remain in the same proportion to each other.

Scale Factor

A scale factor is used to describe an enlargement. It describes how much larger (or smaller) the enlarged shape is compared to the original shape.

Enlarge a Shape

To enlarge a shape, find the distance between each point on the shape and the center of enlargement. The corresponding points on the enlarged shape are this distance multiplied by the scale factor.

Enlarge a Shape with a Fractional Scale Factor

When you enlarge a shape with a fractional scale factor, the shape will be made smaller.

Enlarge a Shape with a Negative Scale Factor

When you enlarge a shape with a negative scale factor, the shape is enlarged on the other side of the center of enlargement and it is turned upside down.

Describe an Enlargement

To describe an enlargement, describe the center of enlargement and the scale factor.

Describe an Enlargement with a Negative Scale Factor

When describing an enlargement with a negative scale factor, remember the center of enlargement is in between the shape and the enlarged shape.

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