R.E.R.TThe four transformations

(Reflections, Enlargements, Rotations & Translations

By Charlotte and Maaheen 7S

http://www.youtube.com/watch?v=v0XUqliEnPQ

You must always specify all the details for each type of transformations. As we go along look out for the specifications.

‘R’ - REFLECTIONS

First, learn how to move shapes around a grid using reflections.

For a reflection you always need to know where the mirror line (or line of symmetry) is.

Mirror line

Y= 0

X= 0

Here are the second most important lines you also need to know.

QUIZ TIME!!

Reflect shape ‘A’ into line X=1

Now reflect shape B into line X=1

‘E’ -EnlargementsThe four key features

- If the scale factor is bigger than 1 then the shape gets bigger.

(NOT TO SCALE)A to B is an enlargement, Scale factor 1 1/2

If the scale factor is smaller than 1 (i.e. a fraction like ½), then the shape gets smaller.

No.2

A B

A to B is an Enlargement of scale factor ½ (Really this is a reduction, but you still call it an enlargement, scale factor ½

(NOT TO SCALE)

NO. 3

(NOT TO SCALE)

A’ B’

5.5 cm 16.5cm

12 cm

4 cm

C’

9 cm

A B

D C3 cm

D’

The Centre of Enlargement

The scale factor also tells you the relative distance of old points and new points from the centre of enlargement.

This is very useful for drawing an enlargement, because you can use it to trace out the positions of the new points from the centre of enlargement, as shown in the diagram.

No. 4The lengths of the two shapes (big and small), are related to the scale factor by this very important formulae triangle which you must learn:

New length

Scale factor x Old length

This now lets you tackle the classic “enlarged photo”, exam question with no difficulty.

PHOTO

9cm

6.4 cm

X cm ENLARGED PHOTO

11.25 cm

To find the width of the enlarged photograph we use the formulae triangle twice, firstly to find the scale factor then to find the missing side:

1) Scale factor = new length Old length = 11.25 9 = 1.25

2) New width = scale factor x old width = 1.25 x 6.4 = 8cm