Rotations
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Transcript of Rotations
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Holt McDougal Geometry
RotationsRotations
Holt Geometry
Warm UpWarm Up
Lesson PresentationLesson Presentation
Lesson QuizLesson Quiz
Holt McDougal Geometry
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Holt McDougal Geometry
Rotations
Identify and draw rotations.
Objective
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Holt McDougal Geometry
Rotations
Remember that a rotation is a transformation that turns a figure around a fixed point, called the center of rotation. A rotation is an isometry, so the image of a rotated figure is congruent to the preimage.
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Holt McDougal Geometry
Rotations
Example 1: Identifying Rotations
Tell whether each transformation appears to be a rotation. Explain.
No; the figure appearsto be flipped.
Yes; the figure appearsto be turned around a point.
A. B.
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Holt McDougal Geometry
Rotations
Check It Out! Example 1
Tell whether each transformation appears to be a rotation.
No, the figure appears to be a translation.
Yes, the figure appears to be turned around a point.
a. b.
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Holt McDougal Geometry
Rotations
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Holt McDougal Geometry
Rotations
Unless otherwise stated, all rotations in this book are counterclockwise.
Helpful Hint
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Holt McDougal Geometry
Rotations
(x, y) →(y,-x)90˚ Clockwise270° Counter Clockwise
(x, y) →(-y,x)90˚ Counter Clockwise270° Clockwise
(x, y) →(y,-x)180˚ same for CC & CW
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Holt McDougal Geometry
Rotations
Example 3: Drawing Rotations in the Coordinate Plane
Rotate ΔJKL with vertices J(2, 2), K(4, –5), and L(–1, 6) by 180° about the origin.
The rotation of (x, y) is (–x, –y).
Graph the preimage and image.
J(2, 2) J’(–2, –2)
K(4, –5) K’(–4, 5)
L(–1, 6) L’(1, –6)
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Holt McDougal Geometry
Rotations
Check It Out! Example 3
Rotate ∆ABC by 180° about the origin.
The rotation of (x, y) is (–x, –y).
A(2, –1) A’(–2, 1)
B(4, 1) B’(–4, –1)
C(3, 3) C’(–3, –3)
Graph the preimage and image.