Translations

A translation is a sliding movement. You can describe a translation using a vector. 

(4) The top number describes the horizontal movement. Positve = right. Negative = left.

(-3) The bottom number describes the verticle movement. Positive = up. Negative = down.

Translated shapes are congruent.

To describe a translation fully you need to write the word 'translation' and the vector. Remember to use positive numbers for movement tot the right or up, and negative for movement to the left or down. You could also say 'Translation 4 squares to the right and 1 square down' But DON'T use the word across to describe a translation. For translations, the lengths of sides and and the angles don't change.

You can reflect a shape in a mirror line. To describe a refelction you need to give the equation of the mirror line. Reflected shapes are congruent. 

It's easy to reflect shapes and check your answers using tracing paper. 

1. Trace the original shape including the mirror line.

2. Turn the diagram so that the mirror line is verticle.

3. Turn the tracing paper over, lining up the mirror lines.

4. Trace the shape in the new postion.

To describe a rotation you need to give:

• The centre of rotation
• The angle of rotation
• The direction of rotation

The centre of rotation is often the origin O. Otherwise it is given as coordinates. The angle of rotation is given as 90 degrees (one quarter turn) or 180 degrees (one half turn). The direction is given as clockwise or anticlockwise. You don't need to give a direction for a rotation of 180 degrees. You're allowed to ask for tracing paper in the exam, this makes it so much easier. Rotated shapes are congruent. 

To describe an enlargement you need to give the scale factor and the center of enlargement. The scale factor of an enlargement tells you how much each length is multiplied by.

Scale factor = enlarged length/original length.

Lines drawn through corresponding points on the object (A) and image (B) meet at the centre of enlargement. When the scale factor is between 0 and 1 image B is smaller than object A. For enlargements, angles in shapes don't change but lengths of sides do change.

1. Draw lines from the centre of enlargement to through each vertex of the shape.

2. For each vertex, multiply the verticle by however much you're asked to.

3. Join up each vertices with a straight line.

Check it:

Each length on the image should be the amount as you mulitpled it by more than the corresponding length on the object. The image is the same as the object, just bigger, so check it looks similar.

1. Count the amount of squares from the ccentre of enlargement to each of the the vertices.

2. Do the necessary calaculations.

3. Make crosses where each of the vertices go.

4. Join them up.

The same checks work on this too.