MA 08 Geometry 6.9 Rotations. 1/4/20166.9 Rotations2 Goals Identify rotations in the plane. Apply...
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Transcript of MA 08 Geometry 6.9 Rotations. 1/4/20166.9 Rotations2 Goals Identify rotations in the plane. Apply...
MA 08 Geometry
6.9 Rotations
04/21/23 6.9 Rotations 2
Goals
Identify rotations in the plane. Apply rotation formulas to figures
on the coordinate plane.
04/21/23 6.9 Rotations 3
Rotation
A transformation in which a figure is turned about a fixed point, called the center of rotation.
Center of Rotation
04/21/23 6.9 Rotations 4
Rotation
Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation.
Center of Rotation
90
G
G’
04/21/23 6.9 Rotations 5
Rotations on the Coordinate Plane
Know the translation formulas for:
•90 rotations
•180 rotations
•clockwise & counter-clockwise
Unless told otherwise, the center of rotation is the origin (0, 0).
04/21/23 6.9 Rotations 6
90 clockwise rotation
Formula
(x, y) (y, x)A(-2, 4)
A’(4, 2)
04/21/23 6.9 Rotations 7
Rotate (-3, -2) 90 clockwise
Formula
(x, y) (y, x)
(-3, -2)
A’(-2, 3)
04/21/23 6.9 Rotations 8
90 counter-clockwise rotation
Formula
(x, y) (y, x)
A(4, -2)
A’(2, 4)
04/21/23 6.9 Rotations 9
Rotate (-5, 3) 90 counter-clockwise
Formula
(x, y) (y, x)
(-3, -5)
(-5, 3)
04/21/23 6.9 Rotations 10
180 rotation
Formula
(x, y) (x, y)
A(-4, -2)
A’(4, 2)
04/21/23 6.9 Rotations 11
Rotate (3, -4) 180
Formula
(x, y) (x, y)
(3, -4)
(-3, 4)
04/21/23 6.9 Rotations 12
Rotation Example
Draw a coordinate grid and graph:
A(-3, 0)
B(-2, 4)
C(1, -1)
Draw ABC
A(-3, 0)
B(-2, 4)
C(1, -1)
04/21/23 6.9 Rotations 13
Rotation Example
Rotate RST 90 clockwise.
Formula
(x, y) (y, x)A(-3, 0)
B(-2, 4)
C(1, -1)
04/21/23 6.9 Rotations 14
Rotate ABC 90 clockwise.
(x, y) (y, x)
A(-3, 0) A’(0, 3)
B(-2, 4) B’(4, 2)
C(1, -1) C’(-1, -1)A(-3, 0)
B(-2, 4)
C(1, -1)
A’B’
C’
04/21/23 6.9 Rotations 15
Rotate ABC 90 clockwise.
Check by rotating ABC 90.
A(-3, 0)
B(-2, 4)
C(1, -1)
A’B’
C’
04/21/23 6.9 Rotations 16
Rotating segments
A
B
C
D
E
F
G
H
O
04/21/23 6.9 Rotations 17
Rotating AC 90 CW about the origin maps it to _______.
A
B
C
D
E
F
G
H
CE
O
04/21/23 6.9 Rotations 18
Rotating HG 90 CCW about the origin maps it to _______.
A
B
C
D
E
F
G
H
FE
O
04/21/23 6.9 Rotations 19
Rotating AH 180 about the origin maps it to _______.
A
B
C
D
E
F
G
H
ED
O
04/21/23 6.9 Rotations 20
Rotating GF 90 CCW about point G maps it to _______.
A
B
C
D
E
F
G
H
GH
O
04/21/23 6.9 Rotations 21
Rotating ACEG 180 about the origin maps it to _______.
A
B
C
D
E
F
G
H
EGAC
A E
C
G
O
04/21/23 6.9 Rotations 22
Rotating FED 270 CCW about point D maps it to _______.
A
B
C
D
E
F
G
H
BOD
O
04/21/23 6.9 Rotations 23
Practice Practice Practice