Chapter 2 I Transformation I,II ENHANCE(1) (1)

7/23/2019 Chapter 2 I Transformation I,II ENHANCE(1) (1)

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2.1 Translation

1. Translation is a transformation that moves all the points on a plane through the same

distance and in the same direction.

2. Properties of a translation

a) the shape, size and orientation of the object and the image are the same

b) every point is moved through the same distance and in the same direction

3. translation is usually e!pressed in the form

k

h, "here h represents the horizontal

movement parallel to the !#a!is and krepresents the vertical movement parallel to

the y# a!is

Example 1

i) $ is mapped onto $% under a

translation

2

&or each point in

triangle is moved & units to the right

follo"ed by 2 uints do"n"ards ii) 'nder the same translation,

image of

( is ((7,5).

Exercise :

i) *ra" the image for each of the

follo"ing object.

ii) +tate the coordinates of the image for each of

the points under the given translation.

1. Translation

,

3

ns"er - )

Transformation I,II 1

x

/H

O 2 4 6

y

A

H

B

0

&

2

y

O 2 4 6

A

0

&

2

y

!

!"#TE$ 2 : T$"%&'O$"TO% ,


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2. Translation

1

23. Translation

2

&

ns"er-

&. Translation

12

ns"er -

. Translation3

ns"er-


C

0

&

2

C0&2 C0&2

ns"er-

O 2 4 6

A

0

&

2

/ *

y

!O 2 4 6 !

C

0

&

2

y

D0

&

2

2 & 0

yy

2 & 0

C

0

&

2

!


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To +in the -ector o+ translation

k

h

n each of the diagram belo", is the image of under translation T

k

h. n each case, state the

vector of translation.

Example 1

Thus, the vector translation is

&

1

3

2

.


4 2 / 2 4

&

2

#2

!

#&

y

Translation-

Translation

Translation-

/

/

Translation

&

i) 4hoose at least t"o corresponding points

bet"een object and image.

ii) 4ount the number of units to move to the

right or left, then the number of units to

move up"ards or do"n"ards.

iii) The vector of translation is

4 2 / 2 4!

&

2

#2

#&

"

"0

& units to the

right

units

do"n"ard

5


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. 0.

2.2 $e+lection

$e+lectionis a transformation "hich reflects all the points on a plane in a line called the axis o+ re+lection.

#roperties o+ re+lection-

i) the shape and size of the object and its image are the same .congruent)

ii) the orientation of the image is laterally inverted compared to the object.

iii) the position of any point lying on the a!is of reflection does not change.

2.2.1 To etermine the imae ner a re+lection

3ra an lael the imae ner a re+lection +or each o+ the +olloin.

Transformation I,II &

4 2 / 2 4

&

2

#2

!

#&

Translation-

4 2 / 2 4

&

2

#2

!

#&

y

n the diagram-

is the image of under a reflection

of y 6a!is or ! 7

P is the image of P under reflection

of line y 714 2 / 2

4

&

2

#2

!

#&

/

/

P

P

y 71

y

4 2 / 2 4

&

2

#2

!

#&

y

4 2 / 2 4

&

2

#2

!

#&

y


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Example- Exercise-

1.

2 3

&

2.2.2 To etermine the axis o+ re+lection

Example- *ra" the a!is of reflection

Exercise

1.

Transformation I,II

8

9 +

!is of reflection

4 2 / 2 4

&

2

#2

!

#&

y

!is of reflection :::

4 2 / 2 4

&

2

#2

!

#&

%

y

4 2 / 2 4

&

2

#2

;

#&

P

5


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a!is of reflection

2. 3

2.2. &tate the axis o+ re+lection.

Example:

!is of reflection - ! 7 2

Exersice

1

!is of reflection -

2.

!is of reflection -

3

!is of reflection -

2. $otation rotation is a transformation "hich rotates all the points on a plane -


%%

4

4

*

*

4 2 / 2 4

&

2

#2

!

#&

y

/ 1 2 4 5 6 7

0

&

!

2

y

0

&

2

! / 1 2 4 5 67

y

4 2 / 24

&

2

#2

!

#&

y


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about a fi!ed point


8/13

2. 9otation of 1? anticloc


9/13

Exercise- *etermine and mar< the centre of

rotation for each of the follo"ing

diagram

1

2

3. &

To etermine centre,anle an irection o+

rotation

4entre - ,)

ngle - =

,*irection - cloc


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2.

4entre - FFFF..

ngle -FFFF. *irection - FFF

4entre - FFFFF..

ngle - FFFFF. *irection - FFF...

&

4entre -FFFFF

ngle - FFFFF

*irection - FFF..

4entre - FFFFF..

ngle - FFFFF.

*irection - FFF...


4 2 / 2 4

&

2

#2

!

#&

y

4 2 / 2 4

&

2

#2

!

#&

y%

"

%

4 2 / 2 4

&

2

#2

!

#&

y

T

T

!

y

4 2 / 2 4

&

2

#2

#&

#

P


11/13

2.4 E%9"$EE%T

n enlargement is a transformation "hich has a fi!ed point call the centre of enlargement.

ll the points on the plane move at a constant ratio from the centre.

The ratio is


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2.

i) +cale factor -

3.

i) +cale factor -

0.

+cale factor -

.

+cale factor -

To ra an imae ner enlarement

*ra" and label an image under the follo"ing

enlargement

Example- centre >,2) and scale factor 2

Exersice

1. 4entre 2,2) and scale factor1

2.


9

%

4

*

%

4

*

9

%

%

@

@

0

&

2

! 2 & 0 >

y

% %

4

40

&

2

2 & 0 !


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2. 4entre 2,&) and scale factor2

1

. entre &,&) and scale factor 2

& 4entre 1,3) and scale factor 3 5 4entre ,) and scale factor 2


0

&

2

! 2 & 0

0

&

2

! 2 & 0

2 & 0 2 & 0

9

y y

+

0

&

2

!

P

0

&

2

!

8

y y

Chapter 2 I Transformation I,II ENHANCE(1) (1)

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