- Sections:
- 0, Chapter 1, Introduction,
### Introduction

After completing this unit you should

- understand how to apply the concept of reflection of a shape in a mirror line
- understand the concept of the rotation of a shape with a given angle, direction and centre
- be confident in making and identifying enlargements of 2-D shapes with given scale factors (and centres of enlargement).

This Unit describes how shapes can be transformed by reflection, rotation and enlargement.

You have three sections to work through and there are check up audits and fitness tests for each section.- Reflections
- Rotations
- Enlargements

- 0, Chapter 2, Reflections,
### Reflections

Reflections are obtained when you draw the image that would be obtained in a mirror.

Every point on a reflected image is always the same distance from the mirror line as the original.

This is shown on the bottom.

**Note:**Distances are always measured at right angles to the mirror line.

- 1, Chapter 2, Task 1, Worked Example 1,
### Worked Example

Use the slider to explore worked examples.

- 1, Chapter 2, Task 2, Exercise 1,
### Exercise

Here are some questions to check your progress; there are more practice questions if needed.

**Exercise 1**Copy the diagrams below and draw the reflection of each object.

**Exercise 2**Copy the diagrams below and draw the reflection of each object.

- 0, Chapter 3, Rotations,
### Rotations

Rotations are obtained when a shape is rotated about a fixed point, called the centre of rotation, through a specified angle.

The diagram shows a number of rotations.

It is often helpful to use tracing paper to find the position of a shape after a rotation.

- 1, Chapter 3, Task 1, Worked Example 2,
### Worked Example

Use the slider to explore worked examples.

- 1, Chapter 3, Task 2, Exercise 2,
### Exercise

Here are some questions to check your progress; there are more practice questions if needed.

1. Copy the axes and shape shown below.

- Rotate the original shape through 90\(^\circ\) clockwise around the point (1, 2).
- Rotate the original shape through 180\(^\circ\) around the point (3, 4).
- Rotate the original shape through 90\(^\circ\) clockwise around the point (1, − 2).
- Rotate the original shape through 90\(^\circ\) anti-clockwise around the point (0, 1).

2. The diagram shows the position of a shape labelled \(A\) and other shapes which were obtained by rotating \(A\).

- Describe how each shape can be obtained from \(A\) by a rotation.
- Which shapes can be obtained by rotating the shape \(E\)?

- 0, Chapter 4, Enlargements,
### Enlargements

An enlargement is a transformation which enlarges (or reduces) the size of an image.

Each enlargement is described in terms of a centre of enlargement and a scale factor.The example shows how the original, \(A\), was enlarged with scale factors \(2\) and \(4\).

A line from the centre of enlargement passes through the corresponding vertex of each image.

The distances, \(OA′\) and \(OA′′\), are related to \(OA\):

\(OA′ = 2 \times OA\)

\(OA′′ = 4 \times OA\)

The same is true of all the other distances between \(O\) and corresponding points on the images. - 1, Chapter 4, Task 1, Worked Example 3,
### Worked Example

Use the slider to explore worked examples.

- 1, Chapter 4, Task 2, Exercise 3,
### Exercise

Here are some questions to check your progress; there are more practice questions if needed

**Exercise 1**Enlarge the shape with scale factor \(2\) using the point marked as the centre of enlargement.

**Exercise 2**Enlarge the triangle shown with scale factor \(3\) and the centre of enlargement shown.

**Exercise 3**For the diagram find the centre of enlargement and the scale factor when the smaller shape

is enlarged to give the bigger shape.

The centre of enlargement is shown on the diagram above. The scale factor is 3.

**Exercise 4**For the diagram find the centre of enlargement and the scale factor when the smaller shape is enlarged to give the bigger shape.

The centre of enlargement is shown on the diagram above. The scale factor is 2.

**Exercise 5**In each example below, the smaller shape has been obtained from the larger shape by an enlargement.

For each example, state the scale factor and the coordinates of the centre of enlargement.a) \(\frac{1}{5}, (8,7)\)

b) \(\frac{2}{3},

(13,9)\)

c) \(\frac{1}{4}, (9,1)\) - 0, Chapter 5, Summary,
### Summary

#### Reflections

are obtained when you draw the image of a shape in a mirror line.

An example is shown below.#### Rotations

are obtained when a shape is rotated about a point,

the centre of rotation, through a specified angle.

For example,#### Transformation

moving a shape so that it is in a different position but retains the same size, area,

angles and line lengths.#### An enlargement

is similar to a transformation but it alters (enlarges or reduces) the size of the

image. An enlargement is described in terms of a scale factor and also a centre of enlargement

which defines the exact location of the image.

For example, the image on the left below has been enlarged by a scale factor of \(2\frac{1}{2}\), with aspecified centre of enlargement.The enlargement opposite (actually a reduction) of scale factor \(\frac{1}{3}\) has no specified centre

of enlargement, so the actual location of the smaller shape could be anywhere.

- 0, Chapter 1, Introduction,
- Interactive Exercises:
- Reflections, Rotations and Enlargements Interactive Exercises, https://www.cimt.org.uk/sif/geometry/g7/interactive.htm
- Reflections, https://www.cimt.org.uk/sif/geometry/g7/interactive/s1.html
- Rotations, https://www.cimt.org.uk/sif/geometry/g7/interactive/s2.html
- Enlargements, https://www.cimt.org.uk/sif/geometry/g7/interactive/s3.html

- YouTube URL: https://youtu.be/JR_Ervr2654

- File Attachments: media/course-resources/Reflections-Rotations-Enlargments_Essential-Informations.pdfmedia/course-resources/Reflections-Rotations-Enlargments_Learning-Objectives.pdfmedia/course-resources/Reflections-Rotations-Enlargments_Text.pdfmedia/course-resources/Reflection-Rotation-Enlargements_PowerPoint-Presentation.pptxmedia/course-resources/Reflections-Rotations-Enlargments_Answers.pdf