Transformation Jamil

8/6/2019 Transformation Jamil

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Transformations I & IIForm 2 & 3

Institut PerguruanPersekutuan Pulau Pinang

(I4P)

KPLI KDC MT (NOV 07)


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Institut PerguruanPersekutuan Pulau

Pinang (I4P)

Transformations I & II

Form 2 & 3


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INDUCTION


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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


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How to get to the public phone ?

Right


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How to get to the public phone ?

Right

Up


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Transformation ITRANSLATION

REFLECTION

ROTATION

Transformation IIENLARGEMENT


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What is

transformation ?

A transformation is a one-to-onecorrespondence between points

in a plane.

A transformation also known as a mapping


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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


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Isometric Transformation

Isometric Transformation transformation

that did not change the shape & measurement of the

object.

Translation

Reflection

Rotation

Isometric

transformation& combination.


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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.


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TranslationTranslation is a transformation which

takes place when points in a plane

are moved in the same direction

through the same distance


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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


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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


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Example :

Translation in the form4

3


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Example :

Determine the image of in the following diagram

under a translation 5-3


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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..


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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


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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


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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


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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


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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


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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


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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


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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


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90

0

B

A

C

AB

C

object image

Example 1

ABC under an clockwise rotationof 90 about the origin

y

x


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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.


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Rotations can be seen in planetary movement.

The concept of rotations can be seen in

wallpaper designs and art work


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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


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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.


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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


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Example: 2

Triangle of diagram 1 is enlargement at

scale factor 3

cente

r

Enlargement at center A


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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


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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.


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EXERCISE


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In the figure below, place the image of triangle L under the

translation.

EXERCISE 1

y

X

-5

2


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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


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Prepared by:Muhammad Jamil Bin Ismail

KPLI-KDC MT NOV 07012-5867131

[email protected]

Mohammad Rosyidi Bin Che PaKPLI-KDC MT NOV 07

019-5454875

[email protected]

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Transformation Jamil