TransformationsMoving a shape or object according toprescribed rules to a new position.

USE the tracing paper provided to help you understand in the exam.

Reflection Rotation Translation Combined Transformations Enlargement (A later presentation)

The shape (A) is reflected in a mirror line so that the new position (shape B) is the same distance from the mirror line but the shape is reversed (mirror image).

Distances from any point to the line are identical.

ReflectionMirror line

A B

X axis reflection

-1

-2

-3

-4

-5

1

2

3

4

5

-1-2-3-4 1 2 3 4 50X->

|̂Y

Axis reflections

Y axis reflection

Reflection in line x = 2

x = 2

Reflection in line y = –1

y = –1

-1

-2

-3

-4

-5

1

2

3

4

5

-1-2-3-4 1 2 3 4 50X->

|̂Y

Reflection on the line y = x

Think about where the line would be!

Measure from the original to the mirror line and then extend to the other side.

RotationThe shape is rotated about a given centre by a given angle and stating whether clockwise or anticlockwise.

B

A

A B = 90O clockwise about the origin (0,0)

A

RotationThe shape is rotated about a given centre by a given angle and stating whether clockwise or anticlockwise.

C

A

A C = 180O clockwise about the origin (0,0)

A

-1

-2

-3

-4

-5

1

2

3

4

5

1 2 3 4 50X->

|̂Y

Translation

A

B

y

x

The “vector” given is written in a large bracket as shown below

This means move the shape in both the ‘x’ and ‘y’ direction. Given as a vector

x translation

y translation

The translation from A to B is given by 1

-6

i.e. 1 across and 6 down

Combined Transformations

Two or more transformations may combine to give ‘something different’.

In this case

two reflections

of ‘A’ can be shown to be a rotation to produce ‘C’

A

BC

Combined Transformations

2 Reflections = 2 Rotations = Reflection + Rotation (90)3 c/w Reflections =

This is particularly useful to remember for the This is particularly useful to remember for the exam!!exam!!

1 Rotation (180)

1 Rotation (add the angles)

= Rotation (180)

1 Reflection (anti-c/w)