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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