1. TRANSFORMATION II
By
Hj Azhari bin Tauhid
Pengetua SEMSAS

2. TRANSFORMATIONS
CHANGE THE POSTION
OF 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

3. TRANSLATION
What does a translation look like?
A TRANSLATION IS A CHANGE IN LOCATION.
x y
Translate from x to y
original image

4. 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)

5. ROTATION
What does a rotation look like?
A ROTATION MEANS TO TURN A FIGURE
centre of rotation

6. ROTATION
This is another way rotation looks
A ROTATION MEANS TO TURN A FIGURE
The triangle
was rotated
around the
point.
centre of rotation

7. ROTATION
Describe how the triangle A was transformed to
make triangle B
A B
Describe the transformation

8. 90o

9. ROTATION
Describe how the triangle A was transformed to
make triangle B
A B
Triangle A was rotated 90 clockwise at the
centre of rotation P(x, y)
P(x, y)

10. 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)

11. REFLECTION
A REFLECTION IS FLIPPED OVER A LINE.
A reflection is a transformation that flips
a figure across a line.

12. 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.

13. CONCLUSION
We just discussed three types of transformations.
See if you can match the action with the
appropriate transformation.
FLIP
SLIDE
TURN
REFLECTION
TRANSLATION
ROTATION

14. 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).

15. TRANSFORMATIONS
CHANGE THE POSTION
OF 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

16. 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.

17. 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.

18. 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’
B
B’
A’
A
=
DA
D’A’
CD
C’D’
BC
B’C’
==

19. 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.

20. Scale factor of enlargement, k
A’
C’
C
B’
B
A
k = A’B’
AB
= 7
4
= 1.75
k = length of image
length of object

21. 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

22. 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

23. 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.

24. 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

25. 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 cm
2 cm
2 cm
F’ H’
1 cm
1 cm
1 cm
Try This

26. 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)

27. Enlarge the figure by a scale factor of 2 with
origin is the centre of enlargement.
2
4
2 4 6 8 10
0
6
8
10
B
C
A
Image Of Enlargement

28. 2
4
2 4 6 8 10
0
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

29. Enlarge the figure by a scale factor of 0.5 with
origin is the centre of enlargement.
2
4
2 4 6 8 10
0
6
8
10
B
C
A
Image Of Enlargement

30. 2
4
2 4 6 8 10
0
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

31. Area Of Image
If k is the scale of an enlargement,
Area of Image
Area of Object
k2 =

32. 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 Object
k2 =
52 = Area of Poster B
600
= 600 x 25Area of Poster B
= 15,000 cm2

33. 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 Object
k2 =
22 = Area of Image
15
= 15 x 4Area of image
= 60 cm2
o
Area of shaded region = 60 - 15
= 45 cm2

34. Look at the pictures below
ENLARGEMENT
Enlarge the image with a scale
factor of 75%
Enlarge the image with a scale
factor of 150%

35. See if you can identify the transformation that
created the new shapes
TRANSLATION

36. See if you can identify the transformation that
created the new shapes
REFLECTIONWhere is the line
of reflection?

37. See if you can identify the transformation that
created the new shapes
ROTATION

38. See if you can identify the transformation that
created the new shapes
ENLARGEMENT

39. The End