8/6/2019 Transformation Jamil
1/40
Transformations I & IIForm 2 & 3
Institut PerguruanPersekutuan Pulau Pinang
(I4P)
KPLI KDC MT (NOV 07)
8/6/2019 Transformation Jamil
2/40
Institut PerguruanPersekutuan Pulau
Pinang (I4P)
Transformations I & II
Form 2 & 3
8/6/2019 Transformation Jamil
3/40
INDUCTION
8/6/2019 Transformation Jamil
4/40
Situation
Michael wants to call his friend, Jalani.Can you tell him how to get to the public
phone ?
Key words :Left Right
Up Down
8/6/2019 Transformation Jamil
5/40
How to get to the public phone ?
Right
8/6/2019 Transformation Jamil
6/40
How to get to the public phone ?
Right
Up
8/6/2019 Transformation Jamil
7/40
Transformation ITRANSLATION
REFLECTION
ROTATION
Transformation IIENLARGEMENT
8/6/2019 Transformation Jamil
8/40
What is
transformation ?
A transformation is a one-to-onecorrespondence between points
in a plane.
A transformation also known as a mapping
8/6/2019 Transformation Jamil
9/40
TRANSFORMATION
Isometric Transformation Non Isometric Transformation
Diagram I is
mapped
to Diagram II withTranslation of
Translation
I
IIb
a
a
b
Reflection
I II
L
L
Diagram I mapped
to Diagram II with
Reflection on
L line
Triangle P is mapped
to Triangle Q with
Rotation of 90clockwise at origin
Rotation
P Q
EnlargementC
C
BBA
ABC is the image
Of ABCwithEnlargement at
A with scale
factor k
8/6/2019 Transformation Jamil
10/40
Isometric Transformation
Isometric Transformation transformation
that did not change the shape & measurement of the
object.
Translation
Reflection
Rotation
Isometric
transformation& combination.
8/6/2019 Transformation Jamil
11/40
Non Isometric Transformation
Enlargement Non isometric transformation
Shape and size differs
But the image obtained through enlargement issimilar to the object. The ratio of image side lengthto its corresponding object side length is a constant.
Ratio of image length size to object length size isknown as enlargement scale factor.
8/6/2019 Transformation Jamil
12/40
TranslationTranslation is a transformation which
takes place when points in a plane
are moved in the same direction
through the same distance
8/6/2019 Transformation Jamil
13/40
Describe a Translation
b
a
Usinghorizontal (left or right)
movement
followed by
vertical (up or down)movement
In form ,
a = horizontal movement
a is negative a is positive
b = vertical movement
b is positive
b is negative
a
b
8/6/2019 Transformation Jamil
14/40
1. Translation. transformation that moves all pointsof a figure the same distance in the same direction
Ex:
3 units to the right
2 units down
SLIDE
8/6/2019 Transformation Jamil
15/40
Example :
Translation in the form4
3
8/6/2019 Transformation Jamil
16/40
Example :
Determine the image of in the following diagram
under a translation 5-3
8/6/2019 Transformation Jamil
17/40
Reflection
A reflection is a transformation which takesA reflection is a transformation which takes
place when all points in a planeplace when all points in a plane (object)(object) areare
flipped over in the same planeflipped over in the same plane (image)(image) at aat a
line known as theline known as the axis of reflectionaxis of reflection..
8/6/2019 Transformation Jamil
18/40
The Concept of Reflection
Object and image are same distance from axis
Same shape
and size
Object and image in
the same size
Axis of Reflection
8/6/2019 Transformation Jamil
19/40
Reflection transformation representing a flipof a
figure in a point, a line or a plane
Y
X
Reflect across
Y - axis
(a)
(b)
A
Reflect across
X- axis
8/6/2019 Transformation Jamil
20/40
Choose A as a key
point and
construct
perpendicular to
the
line PQ passingthrough A.
Determine the image of an object.
Mark point A on the
line, so A and A are
equidistance from
PQ
Step 1
Example:
P
C
D
A
Q
Step 2
B
B
A
D
C
P
Q
8/6/2019 Transformation Jamil
21/40
Determine the image of an object.
Repeat Step 1 and
Step 2 for vertices
B, C and D
Join all the
points.
Step 3
Step 4
A
B
C
D
A
B
C
D
A
P
P
Q
Q
B D
C
8/6/2019 Transformation Jamil
22/40
Determining the coordinates under a
reflection :There are 2 type coordinates under areflection :
a) The coordinates of the image.
b) The coordinates under the object.
) Th di t d th i
8/6/2019 Transformation Jamil
23/40
a) The coordinates under the image.Example :
Find the coordinates of the point P (-3, 2) under a reflection in x-axis and y-axis
Coordinates of the image
under reflection of y-axis
Coordinates of the
image under
reflection of x-axis
Y
X
8/6/2019 Transformation Jamil
24/40
b) The coordinates of the object Find the coordinates of the object that are mapped onto Q(3,-1)
under a reflection in the line MN
The coordinates of the object that are mapped onto Q are (-1,3)
Q(-1,3)
Q (3,-1)
Image is
perpendicular
distance to the image
Draw a perpendicular
bisector line to the line
give (axis of reflection)
M
N
2
2
Y
X
8/6/2019 Transformation Jamil
25/40
8/6/2019 Transformation Jamil
26/40
EXPLORE THE CONCEPT OF ROTATION
EXAMPLE
Students try to explore using other shape.
A rotation is a transformation which takes placewhen all points in a plane are rotated about a point
in the same direction through the same angle
8/6/2019 Transformation Jamil
27/40
90
0
B
A
C
AB
C
object image
Example 1
ABC under an clockwise rotationof 90 about the origin
y
x
8/6/2019 Transformation Jamil
28/40
When you are riding on a
ferries wheel, you are
experiencing a rotation.
Amusement park swings
allow you to experience a rotation.
Rotations can be seen in nature.
The leaf on this plant illustrates the concept of a rotation.
The center of rotation is the point wherethe leaf is attached to the stem.
8/6/2019 Transformation Jamil
29/40
Rotations can be seen in planetary movement.
The concept of rotations can be seen in
wallpaper designs and art work
8/6/2019 Transformation Jamil
30/40
Properties Of a Rotation
1. The shape, sizes and orientation of the
object and its image are the same.
2. The centre of rotation is the only point thatdoes not change its position under the
rotation.
3. An object and its image are equidistant fromthe centre of rotation
8/6/2019 Transformation Jamil
31/40
8/6/2019 Transformation Jamil
32/40
Identify an Enlargement
Enlargement is a type of transformation whereby all
the points of an object move from a fixed point at aconstant ratio.
The fixed point is known as the centre of enlargement.The constant ratio is known as the scale factor.
8/6/2019 Transformation Jamil
33/40
Example: 1Triangle A is enlargement at scale factor 2
Under an enlargement, all the points of an object move from afixed point at a constant ratio.Centre of enlargement (0, 1)This constant ratio is known as the scale factor.
cente
r
8/6/2019 Transformation Jamil
34/40
Example: 2
Triangle of diagram 1 is enlargement at
scale factor 3
cente
r
Enlargement at center A
8/6/2019 Transformation Jamil
35/40
Formulae
Scale factor k = Distance from image to centre of enlargementDistance from object to centre of enlargement
Example: 1Triangle A is enlargement at scale factor 2
Example: 2Triangle of diagram 1 is enlargement at scale factor 3
8/6/2019 Transformation Jamil
36/40
Properties Of Enlargement
The image of an enlargement is similar in shape tothe original object, bur different in size.
The corresponding sides are parallel.
The image and object are similar figures.
The centre of enlargement is a fixed point or aninvariant point.
8/6/2019 Transformation Jamil
37/40
EXERCISE
8/6/2019 Transformation Jamil
38/40
In the figure below, place the image of triangle L under the
translation.
EXERCISE 1
y
X
-5
2
8/6/2019 Transformation Jamil
39/40
In the diagram below, triangles labeled I, II and III are the images of the
colored triangle after transformation. Choose the image of colored triangleafter rotation 90 anti clockwise at the origin.
EXERCISE 2
y
X
P d b
8/6/2019 Transformation Jamil
40/40
Prepared by:Muhammad Jamil Bin Ismail
KPLI-KDC MT NOV 07012-5867131
Mohammad Rosyidi Bin Che PaKPLI-KDC MT NOV 07
019-5454875
Top Related