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9/17/2013



Techniques

Understanding clockwise andanticlockwise rotation

Rotation of a point

Rotation of an object

Determine the rotation point.

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Langkah 1: Mark center

Langkah 2: Find x, Find y

Langkah 3: Rotate

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y

x 2 4-2- 4 0

- 2

- 4

2

4

Find the coordinates of the image of point A under arotation through 90° clockwise about the point R.

A

R

CLOCKWISE

ROTATION

Rotation?

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Example 1:



Example 2:Find the coordinates of the image of point B under arotation through 90° anticlockwise about the point R.

y

x 2 4-2- 4 0

- 2

- 4

2

4

B

R

ANTICLOCKWISE

ROTATION

Rotation?

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Example 3:Find the coordinates of the image of point C under arotation through 90° clockwise about the point R.

y

x 2 4-2- 4 0

- 2

- 4

2

4

R

C

Rotation?

CLOCKWISE

ROTATION

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Example 4:Find the coordinates of the image of point D under arotation through 90° anticlockwise about the point R.

y

x 2 4-2- 4 0

- 2

- 4

2

4

D

R

Rotation?

ANTICLOCKWISE

ROTATION




Example 5:Find the coordinates of the image of point E under arotation through 90° clockwise about the point R.

E

R

y

0 x 2-2

2

4

Step 1

Step 2

Step 3

Palangkan

PUSAT

x = 1

y = 1

Carikan nilai x dan y Rotate

E’

x = 2y = 2

y = 3


y = 3

x = 2

x = 3

y = 2

x = 3

y = 2

The coordinates of the imageof point G is ( 3, 2 ).



Example 6:Find the coordinates of the image of point F under arotation through 90° anticlockwise about the point R.

F

R

y

0 x 2-2

2

4

Step 1

Step 2

Step 3

PalangkanPUSAT

x = 2 y = 1


F’

x = 1

y = 2

y = 3

y = 4


y = 4

x = 2

x = 4y = 2

x = 4y = 2

The coordinates of the imageof point G is ( -4, 2 ).



y

x 2 4-2- 4 0

- 2

- 4

2

4

Example 7:

Find the coordinates of the image of point G under a rotationthrough 90° anticlockwise about the point R.

G

R

Step 1

Step 2

Step 3

Palangkan

PUSAT

x = 1y = 1


G’ The coordinates of the imageof point G is (-2, -3).

y = 2

y = 3

x = 2 x = 3 x = 4


y = 3

x = 4

x = 3y = 4 x = 3y = 4



y

x 2 4-2- 4 0

- 2

- 4

2

4

Example 8:

Find the coordinates of the image of point H under a rotationthrough 90° clockwise about the point R.

H

R

Step 1

Step 2

Step 3

Palangkan

PUSAT

x = 1y = 1


H’

The coordinates of the imageof point E is (4, 2).

x = 2 x = 3 x = 4y = 2

y = 3

y = 4

y = 5


y = 5

x = 4

x = 5y = 4 x = 5y = 4



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Example 9:Find the image of triangle ABC under a rotation

through 90°

clockwise about the origin.A B C

L 1

L 2

L 3

Finish

PalangkanPUSAT

y

0 x 2-2

4

2

Carikan nilai x dan y

123

x = 3

1

2

3

4

y = 4

x = 4

y = 3

x = 4

y = 3

1 2 3 41

2

3

A A’

Putar

B

L 2

L 3


123

x = 3

1

y = 1

x = 1

y = 3

x = 1

y = 3

1

2

3

1

B’ Putar

C


1

x = 1

1

y = 1

x = 1

y = 1

x = 1

y = 1

1

L 2

L 3

Rotate

1C’



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Example 10:Given that A’B’C’ is the image of ABC under a rotation

Find the center of rotation R.

y

0 x 2-2

2 A’

B’

C’

A

B

C

CHOOSE A POINT

A

Step 1

Step 2

Step 3

R

Step 4

The rotation of thepoint is half of x

and half of y fromthe cross.

Measue the x andy from the object

to the image

Cross at the half of x -distance and y-

distance

Estimate the rotationpoint by demining thedirection of the point

2 units

2 units

Pusatputaran

x = 1

y = 1

x = 1

y = 1

x 2

2

APusat

putaran

B

StepB1

StepB2

StepB3

Step

B4

4 units

2 units

Pusatsementara

x = 1

y = 2

x = 2

y = 1

Pusatsementara x 2

Center ofRotation

C

StepC1

StepC2

StepC3

Step

C4

4 units

4 units

Pusatsementara

x = 2

y = 2

x = 2

y = 2

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MATHS IS FUN & EASY !!!

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Ch13transformation 121125051449 Phpapp01 Copy