Transformations

Rotation:

When performing a rotation we need 3 pieces of information:

A centre of rotation (either given as a point or sometimes described as the origin which is the point (0,0))

A direction - either clockwise or anti clockwise (Unless the angle is 180 degrees where it doesn't matter)

An angle.

To perform a rotation use tracing paper and trace your shape, place your pencil on the centre of rotation and rotate the given angle in the given direction to see where the shape is rotated to.

Reflection:

When performing a reflection we need to know which line is the mirror line.  This will either be given on the question or expressed as an equation of a line.

Remember x = 2 is a vertical line which passes through the x axis at the point 2 and y = 3 would be a horizontal line which passes through the y axis at the point 3.

A reflection should look like a mirror image and a mirror can be used if you need extra help.

Translation:

A translation is where an object is moved (without reflecting, rotating or enlarging).  Usually the translation will be described by a vector, where the top number represents the x direction and the bottom number the y direction.

Enlargement:

There are two types of enlargement, one without a centre and one with.
A basic enlargement requires you to enlarge a shape by a given scale factor but it doesn't matter where the shape is drawn.  If a shape is enlarged by scale factor 3, each side of the original shape needs to be multiplied by 3 to give the enlargement.

An enlargement from a given centre requires you to draw an enlargement the centre also specifies where the shape should be drawn.

See the example below:

Sometimes an enlargement can make a shape smaller, but this is still called an enlargement, this happens when the scale factor is between 0 and 1.

Describing a transformation

When you describe a transformation you need to look at what has happened to the original shape.  Has it been turned (it's a rotation), flipped (a reflection), made bigger or smaller (an enlargement) or simply just moved (a translation).  You will also need to describe how so if it's a rotation remember the 3 bits of information needed 1) Centre 2) Direction 3) Angle.  If it is a reflection write down the mirror line as an equation.  If it is an enlargement write down the centre and the scale factor and if it's a translation write down the vector by which it has been translated.