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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
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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?
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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?
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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
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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
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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
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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
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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
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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
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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
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Try Again All the Exercises Available in your module.
11/25/12 PPMP PMR - JOHOR 2009
