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# Ch13 transformation

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11/25/12 PPMP PMR - JOHOR 2009 Techniques

Understanding clockwise and anticlockwise rotation

Rotation of a point

Rotation of an object

Determine the rotation point.

11/25/12 PPMP PMR - JOHOR 2009 Langkah 1: Palang Pusat Langkah 2: Kira x, Kira y Langkah 3: Putar 11/25/12 PPMP PMR - JOHOR 2009 Find the coordinates of the image of point A under a rotation through 90° clockwise about the point R.

A

R

CLOCKWISE ROTATION

Rotation?

Example 1: Example 2:Find the coordinates of the image of point B under a rotation through 90° anticlockwise about the point R.

B

RANTICLOCKWISE

ROTATION

Rotation? Example 3:Find the coordinates of the image of point C under a rotation through 90° clockwise about the point R.

R

C

Rotation?

CLOCKWISE ROTATION Example 4:Find the coordinates of the image of point D under a rotation through 90° anticlockwise about the point R.

D

R

Rotation?

ANTICLOCKWISE ROTATION Example 5:Find the coordinates of the image of point E under a rotation through 90° clockwise about the point R.

E

R

y

0 x2-2

2

4

Langkah 1

Langkah 2

Langkah 3

Palangkan PUSAT

x = 1

y = 1

Carikan nilai x dan yPutar

E’

x = 2

y = 2

y = 3

y = 3

x = 2

x = 3y = 2

x = 3

y = 2

The coordinates of the image of point G is ( 3, 2 ). Example 6:Find the coordinates of the image of point F under a rotation through 90° anticlockwise about the point R.

F

R

y

0 x2-2

2

4

Langkah 1

Langkah 2

Langkah 3

Palangkan PUSAT

x = 2y = 1

Carikan nilai x dan yPutar

F’

x = 1y = 2

y = 3

y = 4

y = 4

x = 2

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

The coordinates of the image of point G is ( -4, 2 ). Example 7:Find the coordinates of the image of point G under a rotation through 90° anticlockwise about the point R.

G

RLangkah 1

Langkah 2

Langkah 3

Palangkan PUSAT

x = 1y = 1

Carikan nilai x dan yPutar

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

y = 2

y = 3

x = 2x = 3x = 4

y = 3

x = 4

x = 3y = 4x = 3y = 4 Example 8:Find the coordinates of the image of point H under a rotation through 90° clockwise about the point R.

H

R

Langkah 1

Langkah 2

Langkah 3

Palangkan PUSAT

x = 1y = 1

Carikan nilai x dan yPutar

H’

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

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

y = 4

y = 5

y = 5

x = 4

x = 5y = 4x = 5y = 4 11/25/12 PPMP PMR - JOHOR 2009

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

Palangkan PUSAT

y

0 x2-2

4

2

Carikan nilai x dan y

123

x = 3

1

2

3

4

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

1 2 3 41

2

3

A

A’Putar

B

L 2

L 3

Carikan nilai x dan y

123

x = 3

1

y = 1x = 1y = 3x = 1y = 3

1

2

3

1

B’Putar

C

Carikan nilai x dan y

1

x = 1

1

y = 1x = 1y = 1x = 1y = 1

1

L 2

L 3

Putar

1C’ 11/25/12 PPMP PMR - JOHOR 2009

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

y

0 x2-2

2A’

B’

C’

A

B

C

CHOOSE A POINT

AA

Step 1

Step 2

Step 3

R

Step 4

The rotation of the point is half of x

and half of y from the cross.

Measue the x and y from the object

to the image

Cross at the half of x-distance and y-

distance

Estimate the rotation point by demining the direction of the point

2 units2 units

2 units2 units

Pusat putaran

x = 1

y = 1

x = 1

y = 1

x2

2

APusat

putaran

BB

Step B1

Step B2

Step B3

Step B4

4 units4 units

2 units2 units

Pusat sementara

x = 1

y = 2

x = 2

y = 1

Pusat sementarax2

Pusat putaran

CC

Step C1

Step C2

Step C3

Step C4

4 units4 units

4 units4 units

Pusat sementara

x = 2y = 2

x = 2

y = 2 