Transformations

Reflections

Lines of symmetry do not always have to touch the object

Mirror line

Object Image

Object

Mirror line

Image

Copy these axes on to squared paper

-5

-4

-3

-2

-1

0

1

2

3

4

5

-5 -4 -3 -2 -1 0 1 2 3 4 5x

y

Plot these points

A(1, 2), B(2, 4) C(5, 1)

A

B

C Reflect triangle ABC in the x-axis to get a new triangle A1B1C1

A1

B1

C1

Reflect triangle ABC in the y-axis to get a new triangle A2B2C2

A2

B2

C2

Reflect triangle ABC in the y = -x to get a new triangle A3B3C3

A3

B3

C3

y x

Join the points to get triangle ABC

Translations

A translation can be thought as a sliding movement

4 squares

Translate the triangle 4 squares to the right

3 squares

Translate the triangle 3 squares upwards

4 squares

Translate the triangle 4 squares to the right and 3 squares upwards

3 squares

This is written as

Translation4

3

Movement right or left

Movement up or down

For translating the triangle 4 squares to the right and 3 squares upwards the movement can be thought as like this

Translation4

3

For translating the triangle 3 squares to the left and 4 squares downwards the movement can be thought as like this

Translation3

4

This is written as

RotationsIn a rotation an object is turned about a point through an angle. The point is called the centre of rotation.

Centre of rotation

A1B1

C1

A

B

C

Anticlockwise rotations are positive and clockwise are negative

Rotate triangle ABC about O through to get a new triangle A1B1C1

90

O

A

B

C

Rotate triangle ABC about O through to get a new triangle A1B1C1

180

O

The centre of rotation can be in different places

Centre of rotationA1

B1

C1

EnlargementAn enlargement changes the size of an object. The change is the same in all directions

Enlarge the rectangle by a scale factor of 2

3 squares

2 squares

6 squares

4 squares

Enlargements are normally done from a centre of enlargement.

O

Measure the distance from the centre O to the vertex A on the triangle

Then multiply this distance by the scale factor. Label this point A1

Repeat for the other vertices B and C

Enlarge the triangle ABC by a scale factor 2. Use O as the centre of enlargement.

AB

C

A1B1

C1

Enlarge the triangle ABC by a scale factor 3. Use O as the centre of enlargement.

The centre of enlargement does not always have to be in the same place

AB

C

O

A1B1

C1

The scale factor can also be less than 1

O

Enlarge the triangle ABC by a scale factor . Use O as the centre of enlargement.

12

AB

C

A1B1

C1

The scale factor can also be less than 0

O

Enlarge the triangle ABC by a scale factor -2. Use O as the centre of enlargement.

Notice that the image A1B1C1 is inverted

B

A

C

A1

B1 C1

To find the mirror line of a reflection given the object and its image

A

B

C

A1

B1

C1

Join two corresponding points on the object and its image AA1

Construct the perpendicular bisector of this line segment

Perpendicular bisector of AA1 i.e. mirror line

A1

B1

C1

A

BC

Centre of rotation

To find the centre of rotation given an object and its image

Join two corresponding points on the object and its image AA1

Draw the perpendicular bisector of this line segment

Repeat for two other corresponding points BB1