TRANSFORMATION II

By

Hj Azhari bin Tauhid

Pengetua SEMSAS

TRANSFORMATIONS

CHANGE THE POSTIONOF A SHAPE

CHANGE THE SIZE OF A SHAPE

TRANSLATION ROTATION REFLECTION

Change in location

Turn around a point

Flip over a line

ENLARGEMENT

Change size of a shape

TRANSLATIONWhat does a translation look like?

A TRANSLATION IS A CHANGE IN LOCATION.

x yTranslate from x to y

original image

In this example, the

"slide" moves the

figure

7 units to the left and 3

units down. (or 3 units

down and 7 units to

the left.)

-7

-3

Or

Translation -7

-3

Example

Translation (-7, -3)

ROTATION

What does a rotation look like?

A ROTATION MEANS TO TURN A FIGURE

centre of rotation

ROTATION

This is another way rotation looks

A ROTATION MEANS TO TURN A FIGURE

The triangle was rotated around the

point.

centre of rotation

ROTATION

Describe how the triangle A was transformed to make triangle B

A B

Describe the transformation

90o

ROTATION

Describe how the triangle A was transformed to make triangle B

A B

Triangle A was rotated 90 clockwise at thecentre of rotation P(x, y)

P(x, y)

ROTATION

Describe how the arrow A was transformed to make arrow B

Describe the transformation.Arrow A was rotated 180 clockwise/

anticlockwise at the centre of rotation P(x, y)

A

BP (x, y)

REFLECTION

A REFLECTION IS FLIPPED OVER A LINE.

A reflection is a transformation that flipsa figure across a line.

REFLECTION

The line that a shape is flipped over is called a line of reflection or axis of reflection.

A REFLECTION IS FLIPPED OVER A LINE.

Line/ axis of reflection

Notice, the shapes are exactly the same distance from the line of reflection on both sides.

The line of reflection can be on the shape or it can be outside the shape.

CONCLUSIONWe just discussed three types of transformations.

See if you can match the action with the appropriate transformation.

FLIP

SLIDE

TURN

REFLECTION

TRANSLATION

ROTATION

Translation, Rotation, and Reflection all change the position of a shape, while the

size remains the same.

The fourth transformation that we are going to discuss is called

ENLARGEMENT (dilation).

TRANSFORMATIONS

CHANGE THE POSTIONOF A SHAPE

CHANGE THE SIZE OF A SHAPE

TRANSLATION ROTATION REFLECTION

Change in location

Turn around a point

Flip over a line

ENLARGEMENT

Change size of a shape

Translation ( )- distance

- direction

x

y- centre P(x, y)

- direction

- angle spins

- Line/axis of

reflection

- distance

- backward

- centre P(x, y)

- scale factor, k

Enlargement changes the size of the shape without changing the shape.

ENLARGEMENT

When you enlarge a photograph or use a copy machine to reduce a map, you are making enlargement with -1< k <1.

Enlarge means to make a shape bigger.

ENLARGEMENT

Reduce means to make a shape smaller.

The scale factor tells you how much something is enlarged or reduced.

Similarity

Similar figures have the same shape:

-All the corresponding angles are equal or

-All the corresponding sides are the same ratio

AB

A’B’

D D’C

C’

BB’

A’

A

=DA

D’A’

CD

C’D’

BC

B’C’==

A scale factor describes how much a figure is enlarged or reduced. A scale factor can be expressed as a decimal, fraction, or percent. A 10% increase is a scale factor of 1.1, and a 10% decrease is a scale factor of 0.9.

Scale factor of enlargement, k

A’

C’

C

B’

B

Ak = A’B’

AB

= 7

4

= 1.75

k = length of image

length of object

A scale factor (k) between 0 and 1 reduces a figure. A scale factor greater than 1 enlarges it.

-1<k<1 image is smaller than the object

-1>k>1 image is larger than the object

k=1 or k=-1 image is equal to the object

-k image and object are in opposite direction

Helpful Hint

Tell whether each transformation is a enlargement.

The transformation is a enlargement.

The transformation is not a enlargement. The figure is distorted.

A. B.

Example: Identifying Enlargement

Every enlargement has a fixed point that is the centre of enlargement. To find the centre of enlargement, draw a line that connects each pair of corresponding vertices. The lines intersect at one point. This point is the centre of enlargement.

Enlarge the figure by a scale factor of 1.5 with P as the center of enlargement.

Multiply each side by 1.5.

Example: Enlarging a Figure

Enlarge the figure by a scale factor of 0.5 with G as the center of enlargement.

G

F H

2 cm 2 cm

2 cm

Multiply each side by 0.5.

G

F H

2 cm2 cm

2 cm

F’ H’

1 cm

1 cm

1 cm

Try This

Determine the centre of enlargement

P(-2, 3)

A’

C’

C

B’

B

A

x

y

-2 864

2

2

6

4

0

-2

Centre of

enlargement, P(-2, 3)

Enlarge the figure by a scale factor of 2 with origin is the centre of enlargement.

2

4

2 4 6 8 100

6

8

10

B

C

A

Image Of Enlargement

2

4

2 4 6 8 100

6

8

10

B’

C’

A’

B

C

A

Image Of Enlargement

Given k = 2,

Origin is the centre of

enlargement

A’B’ = AB x k

= 2 x 2

= 4 unit

Enlarge the figure by a scale factor of 0.5 with origin is the centre of enlargement.

2

4

2 4 6 8 100

6

8

10

B

C

A

Image Of Enlargement

2

4

2 4 6 8 100

6

8

10

B

C

A

B’

C’

A’

Image Of Enlargement

A’B’ = AB x k

= 4 x 0.5

= 2 unit

Given k = 0.5,

Origin is the centre of

enlargement

Area Of Image

If k is the scale of an enlargement,

Area of Image

Area of Objectk2 =

Skill Practice

Poster B is an enlargement of A with scale factor 5. If the area of

poster A is 600cm2,.find the area of poster B.

Area of Image

Area of Objectk2 =

52 = Area of Poster B

600

= 600 x 25Area of Poster B

= 15,000 cm2

Skill Practice

In the figure, the bigger circle is the Image

of the smaller circle under an enlargement

centre O and scale factor 2, Given that the

area of the smaller circle is 15 cm2,

calculate the area of the shaded region

Area of Image

Area of Objectk2 =

22 = Area of Image

15

= 15 x 4Area of image

= 60 cm2

o

Area of shaded region = 60 - 15

= 45 cm2

Look at the pictures below

ENLARGEMENT

Enlarge the image with a scale factor of 75%

Enlarge the image with a scale factor of 150%

See if you can identify the transformation that created the new shapes

TRANSLATION

See if you can identify the transformation that created the new shapes

REFLECTIONWhere is the line of reflection?

See if you can identify the transformation that created the new shapes

ROTATION

See if you can identify the transformation that created the new shapes

ENLARGEMENT

The End