Transformations

Translations

With a translation you just move all the points that make up a shape.

Usually a translation is written like this:

All you do is move each point x units to the right (move left if it is minus) and y units up (move down if is negative).

Rotations

With these you need to give:

• the angle or rotation
• whether it is clockwise or anticlockwise
• the centre of rotation

Here we have a rotation of 90° clockwise about point (0,-1).

Reflections

This is just where one shape is a reflation of another in a given line. This line might be the x axis, y axis or a line with another equation. Below there is a reflection in the line y = x.

Enlargements

When working with these you need to find a scale factor and centre of enlargement.

A handy way to work out the scale factor is to divide the length of one of the new sides by the same side on the old shape.

The centre of enlargement tells you where the enlargement is being measured from. Here’s an example of a shape enlarged by a factor of 2 from centre of enlargement (0,0).If the scale factor is greater than one then the shape gets bigger. If it is less than one the shape gets smaller.

If it is negative the shape is on the opposite side of the centre of enlargement. For example below you have an enlargement of -2 about the origin.Enlargements and Area

If a shape is enlarged by a scale factor of n then:

• Its sides are n times bigger
• Its area is n squared times bigger
• Its volume is n cubed times bigger if it is 3D

So, and this might come up if you are asked to work out a scale factor:

• n equals new side length divided by old side length
• n squared equals new area divided by old area
• n cubed equals new volume divided by old volume