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TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Transformations

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Contents 1 Transformations 2 Translations 3 Reflections 4 Rotation 5 Enlargements 5.1 Example 6 Comments

Transformations

A transformation is an action which changes the position, orientation or size of shape. There are four main types of transformation seen in maths at KS3 and GCSE: translation, reflection, rotation and enlargement.

Translations

A translation occurs when a shape has been moved from one place to another. It is equivalent of picking up the shape and putting it down somewhere else. Vectors are used to describe such transformations.

The image above shows a column vector. It means move the shape 2 units horizontally in the x-axis and move 9 units vertically in the y-axis.

Reflections

When describing a reflection, you need to state the line which the shape has been reflected in.

The blue triangle is the original triangle. To get the green triangle, the blue triangle has been reflected in the x-axis. To get the red triangle, the blue triangle has been reflected in the y-axis.

Rotation

When describing a rotation, the centre and angle of rotation are given. If you wish to use tracing paper to help with rotations: draw the shape you wish to rotate onto the tracing paper and put this over shape. Push the end of your pencil down onto the tracing paper, where the centre of rotation is and turn the tracing paper through the appropriate angle. The resultant position of the shape on the tracing paper is where the shape is rotated to.

The blue triangle is the ordinary triangle. To get to the green triangle it that been rotated 90° clockwise through center of origin.

Enlargements

Enlargements have a centre of enlargement and a scale factor.

1) Draw a line from the centre of enlargement to each vertex ('corner') of the shape you wish to enlarge. Measure the lengths of each of these lines.

2) If the scale factor is 2, draw a line from the centre of enlargement, through each vertex, which is twice as long as the length you measured. If the scale factor is 3, draw lines which are three times as long. If the scale factor is 1/2, draw lines which are 1/2 as long.

Example

The centre of enlargement is marked. Enlarge the triangle by a scale factor of 2.

Comments

What we need here is more detailed explanations with illustrations and examples.

A new article on congruences also is needed links to and from this article. At a very minimum, the article needs to look at the congruence (or lack of congruence in some cases) between shapes than their transformed images.