12-5 graphing rotations course 1 warm up warm up lesson presentation lesson presentation problem of...
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12-5 Graphing Rotations
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Warm UpParallelogram ABCD has vertices (-4, 1), (0, 1), (–3, 4), and (1, 4).
1. What are the vertices of ABCD after it has been reflected across the x-axis?
2. What are the vertices after is has been reflected across the y-axis?
(–4, –1), (0, –1), (–3, –4), (1, –4)
(4, 1), (0, 1), (3, 4), (–1, 4)
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12-5 Graphing Rotations
Problem of the Day
If each of the capital letters of the alphabet is rotated a half turn around its center, which will look the same?
H, I, N, O, S, X, Z
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12-5 Graphing Rotations
Learn to use rotations to change positions of figures on a coordinate plane.
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12-5 Graphing Rotations
You can rotate a figure about the origin or another point on a coordinate plane.
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12-5 Graphing Rotations
A rotation is the movement of a figure about a point. Rotating a figure “about the origin” means that the origin is the center of rotation.
Remember!
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12-5 Graphing Rotations
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
Additional Example 1: Rotating Figures on a Coordinate Plane
E F
GH
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12-5 Graphing Rotations
Give the coordinates of the vertices of the figure after the given rotation. Rotate parallelogram EFGH clockwise 90° about the origin.
Additional Example 1 Continued
The new x-coordinates are the old y-coordinates.
The new y-coordinates are the opposites of the old x-coordinates.
EFGH E’F’G’H’
E(–4, 0) E’(0, 4)
F(0, 0) F’(0, 0)
G(–2, –3) G’(–3, 2)
H(–6, –3) H’(–3, 6)
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12-5 Graphing Rotations
Additional Example 1 Continued
Rotate parallelogram EFGH 90° about the origin.
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
xE F
GH
F’
E’
G’
H’
Course 1
12-5 Graphing Rotations
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
Try This: Example 1
Give the coordinates of the vertices of the figure after the given rotation. Rotate parallelogram EFGH counterclockwise 180° about the origin.
E F
GH
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12-5 Graphing Rotations
Try This: Example 1 Continued
The new x-coordinates are the opposites of the old x-coordinates.
The new y-coordinates are the opposites of the old y-coordinates.
EFGH E’F’G’H’
E(–4, 0) E’(4, 0)
F(0, 0) F’(0, 0)
G(–2, –3) G’(2, 3)
H(–6, –3) H’(6, 3)
Course 1
12-5 Graphing Rotations
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
Try This: Example 1 Continued
Rotate parallelogram EFGH counterclockwise 180° about the origin.
E F
GH
E’F’
G’ H’
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12-5 Graphing Rotations
Additional Example 2A: Art Application
An artist draws this figure. She rotates the figure without changing its size or shape. Give the coordinates of the vertices of the figure after a clockwise rotation of 90° about the origin.
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
C
DB
A E
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12-5 Graphing Rotations
ABCDE A’B’C’D’E’
A(0, 0) A’(0, 0)
B(1, 4) B’(4, –1)
C(3, 5) C’(5, –3)
D(7, 3) D’(3, –7)
Additional Example 2A Continued
E(6, 0) E’(0, –6)
The new x-coordinates are the old y-coordinates.
The new y-coordinates are the opposites of the old x-coordinates.
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12-5 Graphing Rotations
Additional Example 2A Continued
Rotate the figure after a clockwise 90° about the origin.
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
C
DB
A E
C’
D’
B’A’
E’
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12-5 Graphing Rotations
B. Give the coordinates of the vertices of the figure after a counterclockwise rotation of 180° about the origin.
Additional Example 2B: Art Application
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
C
DB
A E
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12-5 Graphing Rotations
The new x-coordinates are the opposites of the old x-coordinates.
The new y-coordinates are the opposites of the old y-coordinates.
Additional Example 2B Continued
ABCDE A’B’C’D’E’
A(0, 0) A’(0, 0)
B(1, 4) B’(–1, –4)
C(3, 5) C’(–3, –5)
D(7, 3) D’(–7, –3)
E(6, 0) E’(–6, 0)
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12-5 Graphing Rotations
Additional Example 2B Continued
Rotate the figure after a clockwise 180° about the origin.
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
C
DB
A E
C’
D’ B’
A’E’
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12-5 Graphing Rotations
Try This: Example 2A
An artist draws this figure. She rotates the figure without changing its size or shape. Give the coordinates of the vertices of the figure after a clockwise rotation of 90° about the origin.
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
C
DB
A E
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12-5 Graphing Rotations
ABCDE A’B’C’D’E’
A(–6, 0) A’(0, 6)
B(–5, 4) B’(4, 5)
C(–3, 5) C’(5, 3)
D(1, 3) D’(3, –1)
Try This: Example 2A Continued
E(0, 0) E’(0, 0)
The new x-coordinates are the old y-coordinates.
The new y-coordinates are the opposites of the old x-coordinates.
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12-5 Graphing Rotations
Try This: Example 2A Continued
Rotate the figure after a clockwise 90° about the origin.
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
C
DB
A E
C’
D’
B’A’
E’
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12-5 Graphing Rotations
B. Give the coordinates of the vertices of the figure after a counterclockwise rotation of 180° about the origin.
Try This: Example 2B
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
C
DB
A E
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12-5 Graphing Rotations
The new x-coordinates are the opposites of the old x-coordinates.
The new y-coordinates are the opposites of the old y-coordinates.
Try This: Example 2B Continued
ABCDE A’B’C’D’E’
A(–6, 0) A’(6, 0)
B(–5, 4) B’(5, –4)
C(–3, 5) C’(3, –5)
D(1, 3) D’(1, –3)
E(0, 0) E’(0, 0)
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12-5 Graphing Rotations
Try This: Example 2B Continued
Rotate the figure after a clockwise 180° about the origin.
-8 -6 -4 -2 2 4 6 8
8
2
4
6
-2
-4
-6
-8
y
x
C
DB
A E
C’D’ B’
A’E’
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12-5 Graphing Rotations
Lesson Quiz
Give the coordinates of the vertices of the trapezoid after the given rotation.
1. Rotate trapezoid ABCD counterclockwise 180° about the origin.
2. Rotate trapezoid ABCD clockwise 90° about the origin.
A’(0, 5), B’(0, 0), C’(–3, 1), D’(–3, 4)
A’(5, 0), B’(0, 0), C’(1, 3), D’(4, 3)
Insert Lesson Title Here
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12-5 Graphing Rotations