Name______________________
[ PACKET
8.3: ROTATIONS ]
1
Write you r q uestions here!
Rotations are exactly as you would expect: a transformation that turns an
image around a given point. When we are graphing, that point will always be the
origin (0,0).
We usually rotate in the same direction that we number the quadrants:
____________________. If you are asked to rotate clockwise, find the equivalent
rotation counterclockwise. (More later…)
B'
A
B'
B
C'
A
C
A
C'
A'
A'
C
ΔABC is rotated 90
about point B
o
B
B
ΔABC is rotated 90
about point A
o
C
ΔABC is rotated 90
about point C
o
Rules for rotating _________________________________ about the origin:
Rule
Rotation of 90 about the origin
o
o
Rotation of 180 about the origin
o
Rotation of 270 about the origin
o
Rotation of 360 about the origin
Abbreviation
Transformation
(x, y) à
R90
R180
R270
R360
°
°
(x, y) à
°
(x, y) à
°
(x, y) à
Please keep in mind:
o
A rotation of 270 COUNTERCLOCKWISE is equivalent to a rotation of _____________________!
o
A rotation of 360 in either direction maps each preimage onto itself.
o
Find the coordinates of ΔA(2, 1), B(3, -1), C(-4, 0) after a rotation of 90 counterclockwise about the
origin. 2 PACKET 8.3: ROTATIONS Write you r q uestions here!
o
Find the coordinates of ΔD(-2, 5), E(0, 4), F(-4, -3) after a rotation of 180 counterclockwise about
the origin.
o
Find the coordinates of ΔG(4, -7), H(-2, 4), F(-1, 0) after a rotation of 90 clockwise about the origin.
a.
b.
Graph trapezoid TRAP where T(0, 4), R(-2,1), A(-5,1), and P(-5,4).
Graph T’R’A’P’, the image of TRAP after R 0 .
c.
Graph kite KITE where K(-3, -3), I(-1, -3), T(-1, -1) and E(-4, 0).
d.
Graph K’I’T’E’, the image of KITE after
270
R90
0
.
6
4
2
-­‐5
5
-­‐2
-­‐4
An object has ____________________if there is a center point around which the
object is rotated a certain number of degrees and the object looks the same.
Examples:
Write you r q uestions here!
[ PACKET
8.3: ROTATIONS ]
Which of the following letters have rotational symmetry?
notes here!
Now, summarize your
Which have reflectional symmetry?
3
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Practice 8.3
Graph and label the image of the figure using the transformation given.
1) rotation 90° counterclockwise about the
origin
2) rotation 180° about the origin
y
y
T
X
M
x
x
N
T
Z
D
Find the coordinates of the vertices of each figure after the given transformation.
3) rotation 90° clockwise about the origin
G(, ), B(, ), U(, )
4) rotation 90° clockwise about the origin
R(, ), F(, ), H(, )
5) rotation 180° about the origin
I(, ), F(, ), C(, )
6) rotation 90° counterclockwise about the
origin
I(, ), X(, ), Q(, )
Worksheet by Kuta Software LLC
-1-
Graph the image and the preimage of the figure using the transformation given.
7) rotation 90° counterclockwise about the
origin
G(, ), B(, ), J(, )
8) rotation 180° about the origin
D(, ), S(, ), Q(, )
y
y
x
x
Graph the image and the preimage of the figure using the transformation given.
9) rotation 90° clockwise about the origin
Worksheet by Kuta Software LLC
y
10) rotation 90° counterclockwise about the
origin
y
F
J
U
x
x
J
S
X
F
-2-
Find the coordinates of the vertices of each figure after the given transformation. Then graph the
reflection.
11) rotation 90° clockwise about the origin
y
12) rotation 180° about the origin
y
E
A
R
F
x
x
V
U
M
13) rotation 90° counterclockwise about the
origin
U(, ), I(, ), C(, ), E(, )
14) rotation 180° about the origin
F(, ), D(, ), V(, ), E(, )
Tell the type of rotation that describes each transformation.
15)
U'
16)
y
G
y
A
H
U
F'
Z
L'
A'
B'
L
B
x
F
x
Z'
H'
G'
17) F(, ), N(, ), V(, ), U(, )
to
F'(, ), N'(, ), V'(, ), U'(, )
Worksheet by Kuta Software LLC
18) Q(, ), A(, ), I(, ), E(, )
to
Q'(, ), A'(, ), I'(, ), E'(, )
-3-
4 PACKET 8.3: ROTATIONS o
1. Find the coordinates of ΔC(-2, 3), A(-3, 4), T(2, 0) after a rotation of 90 counterclockwise about the origin.
2. Graph the image and the preimage of the figure after a rotation of 90o clockwise about the origin. 3. Name 3 letters that do not have rotational symmetry. 4. Name 3 letters that do have rotational symmetry. 5. Sully has a lot of hobbies, but he likes nothing more than his paper-­‐folding club: Coreygami! Currently the club has (18,987,310)0 members. For this application problem, you will get a chance to join Coreygami. To join, you must create a figure with rotational symmetry using Coreygami. The choice is yours: you can certify yourself as an "Amateur," "Professional," "Warrior," or "Supreme-­‐Jedi-­‐Master" Coreygamist. Those that complete the "Supreme Jedi Master" receive a personalized laser-­‐printer-­‐signed certificate from the Algebros. To complete the application task, go to the 8.3 section page, and choose one of the tasks below the lesson video. You must follow the directions carefully. After you have completed your application task, answer the following questions: a.
Your origami product has several "points" of symmetries. How many "points" are there? b.
Divide 360 degrees by the number of symmetrical "points" in your product. This is called the angle of rotation. What is the angle of rotation of your product? c. Write your name on your creation. Your masterpiece will be displayed for all to admire!