Name: Date: © Marshall Cavendish International (Singapore) Private Limited. 36 Chapter 8 Lesson 8.3 Lesson 8.3 Rotations Solve. Show your work. 1. A rotation of point P in the direction indicated about O maps P onto P9. State the angle of rotation. a) Counterclockwise b) Clockwise x y 1 1 2 3 1 2 3 4 O 1 2 P P x y 1 1 2 3 2 3 4 1 2 3 4 O 1 2 P P 2. Each point has been rotated about the origin, O to form its image. State the angle and the direction of each rotation. a) b) x y 1 1 2 3 2 3 4 1 2 O 1 2 3 4 P P x y 1 1 2 3 2 3 1 2 3 O 2 1 3 Q Q
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Name: Date:
© M
arsh
all C
aven
dish
Inte
rnat
iona
l (Si
ngap
ore)
Priv
ate
Lim
ited.
36 Chapter 8 Lesson 8.3
Lesson 8.3 Rotations
Solve. Show your work.
1. A rotation of point P in the direction indicated about O maps P onto P9. State the angle of rotation.
a) Counterclockwise b) Clockwise
x
y
1�1�2�3
1
2
3
4
O�1
�2
P
P�
x
y
1�1�2�3 2 3 4
1
2
3
4
O�1
�2
P�
P
2. Each point has been rotated about the origin, O to form its image. State the angle and the direction of each rotation.
a) b)
x
y
1�1�2�3 2 3 4
1
2
O�1
�2
�3
�4P�
P
x
y
1�1�2�3 2 3
1
2
3
O
�2
�1
�3Q�
Q
(M)MIFEPC3B_08.indd 36 17/08/12 10:20 AM
Name: Date: ©
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
rivat
e Li
mite
d.
Extra Practice Course 3B 37
Solve. Show your work.
3. Peter is in the seat of a Ferris wheel rotating about its center O. The seat is at a point P. He is rotated from P by each of the following rotations. Draw and label his positions after each rotation from P on the coordinate grid.
a) A: clockwise rotation of 180°
b) B: clockwise rotation of 270°
c) C: counterclockwise rotation of 90°
d) D: counterclockwise rotation of 45°
x
y
1�1�2�3�4 2 3 4
1
2
3
4
O�1
�4
�3
�2
P
(M)MIFEPC3B_08.indd 37 17/08/12 10:20 AM
Name: Date:
© M
arsh
all C
aven
dish
Inte
rnat
iona
l (Si
ngap
ore)
Priv
ate
Lim
ited.
38 Chapter 8 Lesson 8.3
Solve. Show your work.
4. A spinner rotates about the center, O of a circular board. Initially, the spinner is in the position represented by OP.
a) If the spinner rotates to the position represented by OA, describe the rotation.
b) A point B (23, 2) undergoes the same rotation. Find the coordinates of its image B9.
c) A point C also undergoes the same rotation. Its image is C9 (21, 23). Find the coordinates of C.
x
y
1�1�2�3�4�5�6 2 3 4 5 6
1
2
3
4
5
6
O�1
�2
�3
�4
�5
�6
P
A
(M)MIFEPC3B_08.indd 38 17/08/12 10:20 AM
Name: Date: ©
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
rivat
e Li
mite
d.
Extra Practice Course 3B 39
Solve. Show your work.
5. The diagram shows the minute hand of a clock rotating about the center, O of the clock face. The minute hand is initially represented by OP. Point P is at position (3, – 4). Find the position of the minute hand under each of the following rotations.
a) Image P9: rotation of 90° counterclockwise
b) Image P: rotation of 90° clockwise
c) Image P999: rotation of 180° counterclockwise
x
y
1�1�2�3�4�5�6 2 3 4 5 6
1
2
3
4
5
6
O�1
�2
�3
�4
�5
�6
P
12 1
2
3
4
56
7
8
9
10
11
(M)MIFEPC3B_08.indd 39 17/08/12 10:20 AM
Name: Date:
© M
arsh
all C
aven
dish
Inte
rnat
iona
l (Si
ngap
ore)
Priv
ate
Lim
ited.
40 Chapter 8 Lesson 8.3
Solve. Show your work.
6. A trapezoid, ABCD, is drawn on the coordinate plane.
x
y
1�1�2�3�4�5 2 3 4 5
1
2
3
4
5
O�1
�2
�3
�4
�5
A D
B C
a) ABCD is rotated 90° counterclockwise about the origin O. Draw and label the image of A9B9C9D9.
b) What are the coordinates of A9, B9, C9, and D9?
c) ABCD is rotated 180° clockwise about the origin, O. Draw and label the image of ABCD.
d) Find the coordinates of A, B, C, and D.
e) How are A9B9C9D9 and ABCD related?
(M)MIFEPC3B_08.indd 40 17/08/12 10:20 AM
Name: Date: ©
Mar
shal
l Cav
endi
sh In
tern
atio
nal (
Sing
apor
e) P
rivat
e Li
mite
d.
Extra Practice Course 3B 41
Solve. Show your work.
7. A regular pentagon ABCDE is rotated about its center O, so that its appearance stays the same, but the vertices are rotated to different positions. The pentagon is rotated so that the vertex A moves to the original position of B. Describe two possible rotations, stating each angle of rotation and the direction.
8. P9Q9 is the image of PQ under a rotation about O. Explain, without using a coordinate grid, how you would obtain the position of O by construction. Show your construction clearly.
P�
Q�
QP
A
B
CD
E
O
(M)MIFEPC3B_08.indd 41 17/08/12 10:20 AM
Related Documents
