Transformations

Learning Outcomes

I can translate, reflect, rotate and enlarge a shape

I can enlarge by fractional and negative scale factors

I can interpret diagrams where transformations have occurred

I can find the centre and scale factor of a given enlargement

I can find the centre direction and angle of a given rotation

0

2

4

6

-6

-4

-2

5 10-10 -5

Transformations ReflectionThe object and its image are always the same perpendicular distance from the mirror line.

A

B C

x axis

y axis

0

2

4

6

-6

-4

-2

5 10-10 -5

Transformations Reflection

Reflect triangle ABC in the line y = x.

A

B C

y = x

0

2

4

6

-6

-4

-2

5 10-10 -5

Transformations Reflection

Reflect triangle ABC in the line y = -x.

A

B C

y = -x

Transformations ReflectionSummary of Reflections

Object points Reflection Image Points

A(1,1) B(1, 3)C(2,2) D(1, 2)

x axis

A(1,-1) B(1, -3)C(2,-2) D(1, -2)

(x, y) → (x, -y)

A(1,1) B(1, 3)C(2,2) D(1, 2)

y axis

A(-1,1) B(-1, 3)C(-2,2) D(1-, 2)

(x, y) → (-x, y)

A(1,1) B(1, 3)C(2,2) D(1, 2)

y = x

A(1,1) B(3, 1)C(2,2) D(2, 1)

(x, y) → (y, x)

A(1,1) B(1, 3)C(2,2) D(1, 2)

y = -x

A(-1,-1) B(-3, -1)C(-2,-2) D(-2, -1)

(x, y) → (-y, -x)

0

2

4

6

-6

-4

-2

5 10-10 -5

Transformations Rotations

Rotation of 90° clockwise about (0, 0)

A

B C

Transformations Rotations

Summary of Rotations

Object Image

A (1, 1) A' (1, -1)

B (1, 3) B' (3, -1)

C (2, 2) C' (2, -2)

D (1, 2) D' (2, -1)

(x, y) → (y, -x)

Object Image

A (1, 1)A' (-1, -

1)

B (1, 3)B' (-1, -

3)

C (2, 2)C' (-2, -

2)

D (1, 2)D' (-1, -

2)

(x, y) → (-x, -y)

Object Image

A (1, 1) A' (-1, 1)

B (1, 3) B' (-3, 1)

C (2, 2) C' (-2, 2)

D (1, 2) D' (-2, 1)

(x, y) → (-y, x)

90º Clockwise at (0,0)

180º (either direction)at (0,0)

90º Anti-Clockwise at (0,0)

Transformations Translations

When a shape is translated its orientation does no change – it looks the same but

is in a different position. A translation is written as a column vector with x

denoting the number of units the shape is moved along the x axis and y denoting

the number of units the shape is moved along the y axis.

y

x

+ve- ve

A translation moves

a shape 5 units to the

right and 2 units up.

2

5

6

0

2

4

5 10

A B

C

Transformations Translations

1. Translate ABCE label the new shape A1B1C1D1

2. Translate A1B1C1D1 label the new shape A2B2C2D2

4

2

2

6

0

2

4

6

-6

-4

-2

5 10-10 -5

A B

DC

A1 B1

D1C1A2 B2

D2C2

Transformations Enlargements

An enlargement has 2 properties1) Centre2) Scale Factor

When a shape is enlarged the image point is found by using the centre and scale factor of the enlargement

PointCentre Point

Scale Factor

Image

A A1(6, 6)

B B1(18, 6)

C C1(18, 12)

12

18

2

2

2

6

4

6

6

6

6

18

2

2

2

6

4

6

With following table shows and enlargement with centre (0, 0) and scale factor 3

TransformationsEnlarging a Shape when centre

of Enlargement is not origin

0

2

4

6

-2

5 10-10 -5

A B

DC

Point Centre → Point Image Point

1

3

1

1

3

1

3

3

D

C

B

A

Enlarge shape ABCD by scale factor 3 centred at (-1, 2)

TransformationsEnlarging a Shape when centre

of Enlargement is not origin

-4

-2

0

2

-6

5 10-10 -5

Point Centre → Point Image Point

1

3

1

1

3

1

3

3

D

C

B

A

Enlarge shape ABCD by scale factor -2 centred at (0, 0)

Additional Notes

Transformations

Learning Outcomes:At the end of the topic I will be able to

Can Revise Do Further

I can translate, reflect, rotate and enlarge a shape

I can enlarge by fractional and negative scale factors

I can interpret diagrams where transformations have occurred

I can find the centre and scale factor of a given enlargement

I can find the centre direction and angle of a given rotation