Transformations

Objective: to develop an understanding of the four transformations.

Starter – if 24 x 72 = 2016, find the value of:

1) 2.8 x 72 = 2) 2.8 x 7.2 = 3) 0.28 x 7.2 =

201.620.16

2.016

What are the four types of transformations?

1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1-1-2-3 -4 -5-6-7-8-9

987654321

x

y

1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1-1-2-3 -4 -5-6-7-8-9

987654321

x

y

1) Draw the line x = 1. Reflect the shape in the line you have drawn.

2) Draw the line x = 3. Reflect the shape in the line you have drawn.

1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1-1-2-3 -4 -5-6-7-8-9

987654321

x

y

1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1-1-2-3 -4 -5-6-7-8-9

987654321

x

y

Reflection

1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1-1-2-3 -4 -5-6-7-8-9

987654321

x

y

1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1-1-2-3 -4 -5-6-7-8-9

987654321

x

y

3) Draw the line x = y. Reflect the shape in the line you have drawn.

4) Draw the line x = y. Reflect the shape in the line you have drawn.

1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1-1-2-3 -4 -5-6-7-8-9

987654321

x

y

1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1-1-2-3 -4 -5-6-7-8-9

987654321

x

y

Reflection

Describing Reflections

2 marks

•1 mark for the type of transformation – reflection

•2nd mark for the mirror line (e.g. x = 1)

Vectors

• Vectors describe translations. They are represented as two numbers on top of each other in brackets.

right

up

Right and up are positive numbers.

left

down

Left and down are negative numbers.

Translation

When an object is moved in a straight line in a given direction we say that it has been translated.

For example, we can translate triangle ABC 5 squares to the right and 2 squares up:

C

A

B

object

C

A

B

object

C

A

B

object

C

A

B

object

C

A

B

object

C

A

B

object

C

A

B

object

C

A

B

object C’

A’

B’

image

Every point in the shape moves the same distance in the same direction.

object

Translations on a coordinate grid

0 1 2 3 4 5 6 7–1–2–3–4–5–6–7

1

2

3

4

5

6

7

–2

–4

–6

–3

–5

–7

–1

Translate the shape 3 squares left and 8 squares down. Label each point in the image.

A’(2, –1)

B’(0, –6)

C’(–5, –2)

y

x

C(–2, 6) A(5, 7)

B(3, 2)

Translations on a coordinate grid

The coordinates of vertex A of this shape are (3, –4).

When the shape is translated the coordinates of vertex A’ are(–3, 3).

What translation will map the shape onto its

image?

6 left7 up

1 2 3 4 5 6–2–3–4–5–6–7

1

2

5

6

–2

–4

–6

–3

–5

–7

–1

y

x7–1

3

4

7

0

A(3, –4)

A’(–3, 3)

Describing Translations

2 marks

• 1 mark for the type of transformation – translation

• 2nd mark for the vector (e.g. )

To enlarge the rectangle by scale factor x2 from

the point shown.

Centre of Enlargement

Object

A B

CD

Or Count Squares

Image

A/ B/

C/D/

Enlargements from a Given Point

1. Draw the ray lines through vertices.

2. Mark off x2 distances along each line.

3. Draw and label image.

The small rectangle has been enlarged as shown.

Find the centre of enlargement.

Object

A

CD

Image

A/ B/

C/D/

B

Draw 2 ray lines through corresponding vertices to locate.

Centre of Enlargement

Finding the Centre of an Enlargement

Describing Enlargements

3 marks

• 1 mark for the type of transformation – enlargement

• 2nd mark for the scale factor (e.g. x2)

• 3rd mark for the centre of enlargement

Rotations on a coordinate grid

The vertices of a triangle lie on the points A(2, 6), B(7, 3) and C(4, –1).

0 1 2 3 4 5 6 7–1–2–3–4–5–6–7

1

2

3

4

5

6

7

–2

–4

–6

–3

–5

–7

–1

A(2, 6)

B(7, 3)

C(4, –1)

Rotate the triangle 180° clockwise about the origin and label each point on the image.

A’(–2, –6)

C’(–4, 1)

What do you notice about each point and

its image?

B’(–7, –3)

Rotations on a coordinate grid

0 1 2 3 4 5 6 7–1–2–3–4–5–6–7

1

2

3

4

5

6

7

–2

–4

–6

–3

–5

–7

–1

A(–6, 7)

B(2, 4)

B’(–4, 2)

Rotate the triangle 90° anticlockwise about the origin and label each point in the image.

C(–4, 4)

A’(–7, –6)

C’(–4, –4)

Describing Rotations

3 marks

• 1 mark for the type of transformation – rotation

• 2nd mark for the angle of turn and state whether its clockwise/anticlockwise (e.g. 90° clockwise)

• 3rd mark for the centre of rotation (e.g. 0, 0)