# Transformations

## Transformations

Transformations, as the name suggests, change things - usually, as far as you're concerned, triangles on a graph.

The 4 main transformations (and the ones you need to know about) are Reflection, Rotation, Enlargement and Translation.

#### Reflection

Despite its name, this doesn't require a great deal of thought! You simply have a line of reflection and move every point on the shape the same distance away on the other side of the line.

If you're doing a reflection on a graph the mirror line may be given as an equation or it might just be the x-axis or the y-axis.

If the mirror line equation is x =..... then it is a vertical line through that number on the x-axis.

If the mirror line equation is y =..... then it is a horizontal line through that number on the y-axis.

y = x is the diagonal line going through (0, 0), (1. 1), (2, 2), etc.

y = -x is the diagonal line going through (0, 0), (1, -1), (2, -2), etc.

Important: Don't try to reflect whole shapes all at once. Reflect each corner on the shape then draw the reflection by joining the points you've reflected.

Try this exercise:

The graph below shows triangle ABC being reflected in the line y = x. Plot the co-ordinates of the reflected triangle by left clicking your mouse on the graph shown.

#### Rotation

This needs 3 pieces of information:

1. Angle (it will probably either be 900 or 180[sip]0).

2. Direction (clockwise or anti-clockwise).

3. Centre of Rotation (a co-ordinate).

Again, rotate each point on the shape before drawing it! Each point stays exactly the same distance from the centre of rotation as if the shape was fixed to the centre of rotation by a piece of wire!

The example below shows the triangle ABC being rotated by 900 clockwise about the origin onto the triangle A'B'C'.

#### Enlargement

This needs 2 pieces of information:

1. Scale factor.

2. Centre of Enlargement.

You draw lines from the centre of enlargement through each corner of the shape. The new enlarged shape will have its corresponding corners on these lines. The scale factor tells you where.

On a graph, it's easier to split distances into 'how far across?' and 'how far up or down?'.

To draw the new shape you multiply the distances of each corner from the centre of enlargement by the scale factor and that is the distance of your new shape from the centre of enlargement.

So, for instance, an enlargement with centre (0,0) and scale factor 3 will move a point at (2,3) to (6,9).

The example below shows an enlargement of triangle ABC with scale factor 2 and centre of enlargement (1,1).

Note: A fractional scale factor leads toa reduction in size. A negative scale factor means you go the opposite direction to draw your new shape.

#### Translation

This needs 1 piece of information - a vector (two numbers on top of one another - the top one is how far across to move, the bottom one is how far up or down to move).

You literally just have to move each point on the shape by the vector and draw your new shape!

For example:

will move each point on a shape 4 across and 3 up.

The example below shows triangle ABC undergoing a translation of