ROTATIONS EQ: How do you rotate a figure 90, 180 or 270 degrees around a given point?
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Transcript of ROTATIONS EQ: How do you rotate a figure 90, 180 or 270 degrees around a given point?
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ROTATIONS
EQ: How do you rotate a figure 90, 180 or 270 degrees around a given point?
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Rotations
Center of Rotation: the point you turn the object around
Angle of Rotation: number of degrees to turn the object
Counter clockwise: always turn to the left (unless it says otherwise)
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90° - ONE TURN
180° - TWO TURNS
270° - THREE TURNS
On the Coordinate Plane
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90˚
Center of Rotation(0, 0)
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180˚
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270˚
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Rotating Polygons about their Center
Full circle = 360˚
360÷5
72˚
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R(2, 5) a) 90° Rotation about the origin
R’ __________
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R(2, 5) b) 180° Rotation about the origin
R’ __________
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R(2, 5) c) 270° Rotation about the origin
R’ __________
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R(-4, 2) a) 90° Rotation about point O
R’ __________
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R(-4, 2) b) 180° Rotation about point O
R’ __________
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R(-4, 2) c) 270° Rotation about point O
R’ __________
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90˚
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180˚
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270˚
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4.) Point R is the center of regular quadrilateral MATH. # of sides: ________Degree of each turn:
_________
a. 90° rotation of H about R # of turns: _____ Image: ______
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b. 180° rotation of M about R # of turns: ______ Image: ______
c. 270° rotation of about R # of turns: ________ Image: ________
d. 360° rotation of about R # of turns: _______ Image: _______
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5.) Point T is the center of regular decagon ABCDEFGHIJ
# of sides: ______ Degree of each turn: _____
a. 72° rotation of H about T # of turns: _____ Image: _____
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b. 180° rotation of D about T # of turns: _______ Image: _______
c. 252° rotation of about T # of turns:_______ Image: _______
d. 360° rotation of about R # of turns: _______ Image: ________
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6.) Point M is the center of the regular hexagon. # of sides: ________ Degree of each
turn: _________
a. What is the angle of rotation that maps H to X?____
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b. What is the angle of rotation that maps E to G?______
c. What is the angle of rotation that maps to ?________
d. What is the angle of rotation that maps
to ?________
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Challenge: Perform the following transformations on the figure below.
1. Reflect over the y-axis
2. (x , y) → (x + 1, y – 8)
3. Rotate 270° about the origin
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In a coordinate plane, find the reflection of (2,−4) over the line y = x.
F (−4,2)
G (4,2)
H (−2,4)
J (4,−2)
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70° Rotation
70°
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90° Rotation
90°
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120° Rotation
120°
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180° Rotation
180°
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270° Rotation
270°
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Rules
A point (x, y) that has been rotated
90˚ (x, y)→(-y, x)
180˚ (x, y)→(-x, -y)
270° (x, y) → (y, -x)
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Practice
Rotate (1, 5) 90˚ →
Rotate (1, 5) 180˚ →
Rotate (1, 5) 270˚ →
Rotate (4, -2) 90˚ →
Rotate (4, -2) 180˚ →
Rotate (4, -2) 270˚ →