ch13transformation 121125051449 phpapp01 copy
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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:
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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
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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
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y = 3
x = 2
x = 3
y = 2
x = 3
y = 2
The coordinates of the imageof point G is ( 3, 2 ).
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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
Carikan nilai x dan y Rotate
F’
x = 1
y = 2
y = 3
y = 4
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y = 4
x = 2
x = 4y = 2
x = 4y = 2
The coordinates of the imageof point G is ( -4, 2 ).
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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
Carikan nilai x dan y Rotate
G’ The coordinates of the imageof point G is (-2, -3).
y = 2
y = 3
x = 2 x = 3 x = 4
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y = 3
x = 4
x = 3y = 4 x = 3y = 4
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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
Carikan nilai x dan y Rotate
H’
The coordinates of the imageof point E is (4, 2).
x = 2 x = 3 x = 4y = 2
y = 3
y = 4
y = 5
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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
Carikan nilai x dan y
123
x = 3
1
y = 1
x = 1
y = 3
x = 1
y = 3
1
2
3
1
B’ Putar
C
Carikan nilai x dan y
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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