Chapter 2 I Transformation I,II ENHANCE(1) (1)
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Transcript of Chapter 2 I Transformation I,II ENHANCE(1) (1)
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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-
Transformation I,II 2
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
.
Transformation I,II 3
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. $otation rotation is a transformation "hich rotates all the points on a plane -
Transformation I,II 0
%%
4
4
*
*
4 2 / 2 4
&
2
#2
!
#&
y
/ 1 2 4 5 6 7
0
&
!
2
y
0
&
2
! / 1 2 4 5 67
y
4 2 / 24
&
2
#2
!
#&
y
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about a fi!ed point
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2. 9otation of 1? anticloc
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Exercise- *etermine and mar< the centre of
rotation for each of the follo"ing
diagram
1
2
3. &
To etermine centre,anle an irection o+
rotation
4entre - ,)
ngle - =
,*irection - cloc
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2.
4entre - FFFF..
ngle -FFFF. *irection - FFF
4entre - FFFFF..
ngle - FFFFF. *irection - FFF...
&
4entre -FFFFF
ngle - FFFFF
*irection - FFF..
4entre - FFFFF..
ngle - FFFFF.
*irection - FFF...
Transformation I,II 1
4 2 / 2 4
&
2
#2
!
#&
y
4 2 / 2 4
&
2
#2
!
#&
y%
"
%
4 2 / 2 4
&
2
#2
!
#&
y
T
T
!
y
4 2 / 2 4
&
2
#2
#&
#
P
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2.4 E%9"$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.
Transformation I,II 12
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
Transformation I,II 13
0
&
2
! 2 & 0
0
&
2
! 2 & 0
2 & 0 2 & 0
9
y y
+
0
&
2
!
P
0
&
2
!
8
y y