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9-3: RotationsRigor: Students will rotate figures about a
point on and off the coordinate plane.
Relevance: Rotations describe movement.
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Rotations• Turn to page 383-384 in your core book and
highlight:
• A rotation turns all points about a point called the center of rotation.
• Rotation is always counterclockwise unless otherwise specified
• Function Notation: r (Q, xo) (pre-image)
center of rotation angle of rotation
• A Rotation is: a rigid transformation, image is the same distance from center as pre-image, all points rotate to image by the same angle of rotation.
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Exploration• On a piece of graph paper, use a straight edge to
draw a coordinate plane with ΔABC with coordinates A(2,3), B(7, 8), and C(4, 5).
• Place a piece of scratch paper on top of Δ ABC and trace it, forming Δ A’B’C’.
• Place your pencil on C (center of rotation) and turn ΔA’B’C’. Notice how ΔA’B’C’ moves in relation to ΔABC.
• Now let the origin be the center of rotation. How does the triangle move differently?
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Special Rotations in the Coordinate PlaneHighlight on pg 385, add function notation
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Examples from the core book
• Rotating about the origin: EX 3 pg 385 (Label vertices A, B, C, D)
• Also rotate ABCD 90o and 1800
• Rotating about another point: EX 2 pg 384 (use tracing paper to check!)
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Rotations in Regular Polygons
• A regular polygon has congruent sides and congruent interior angles.
• You can divide any regular polygon into congruent triangles.
• When you rotate a regular polygon about its center, the sides will line up when you rotate it a certain number of degrees, called the central angle.
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ExamplePoint X is the center of the regular polygon PENTA. What is the image for the given rotations?
A) 72o rotation of E about X.
B) r (216o, X) ()
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Real Life Example
The London Eye observation wheel takes 30min to make a complete rotation. What is the angle of rotation of a car after 5 minutes? How many minutes would it take for the car to rotate 270o?
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9-3 Classwork/Homework• 9-3 Classwork from the core book:
• pg 386-387 #1 – 3, 5 – 8
• 9-3 Homework from the core book:
• Pg 389 #5 – 10
• Pg 390 #1, 3, 4, 5, 7