9-3
9-3 Rotations
Rotations
Warm Up
Lesson Presentation
Lesson Quiz
HoltMcDougal
GeometryGeometry
Holt
9-3 Rotations
Warm Up
1. The translation image of P(–3, –1) is
P’(1, 3). Find the translation image of
Q(2, –4). Q’(6, 0)
Holt McDougal Geometry
9-3 Rotations
Objective
Identify and draw rotations.
Holt McDougal Geometry
9-3 Rotations
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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.
Holt McDougal Geometry
9-3 Rotations
Example 1: Identifying Rotations
Tell whether each transformation appears to
be a rotation. Explain.
A.
B.
No; the figure appears
to be flipped.
Yes; the figure appears
to be turned around a
point.
Holt McDougal Geometry
9-3 Rotations
Check It Out! Example 1
COPY THIS SLIDE:
Tell whether each transformation appears to
be a rotation.
b.
a.
No, the figure appears
to be a translation.
Holt McDougal Geometry
Yes, the figure
appears to be turned
around a point.
9-3 Rotations
COPY THIS SLIDE:
Holt McDougal Geometry
9-3 Rotations
Helpful Hint
Unless otherwise stated, all rotations in this book
are counterclockwise.
Holt McDougal Geometry
9-3 Rotations
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BY 270o ABOUT THE ORIGIN
(x, y)(y, -x)
Holt McDougal Geometry
9-3 Rotations
Example 3: Drawing Rotations in the Coordinate
Plane
COPY THIS SLIDE:
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).
J(2, 2)
J’(–2, –2)
K(4, –5)
K’(–4, 5)
L(–1, 6)
L’(1, –6)
Graph the preimage and image.
Holt McDougal Geometry
9-3 Rotations
Check It Out! Example 3
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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.
Holt McDougal Geometry
9-3 Rotations
COPY THIS SLIDE: Examples:
Rotate ∆RST with vertices R(–1, 4), S(2, 1),
and T(3, –3) about the origin by the given
angle.
1. 90°
R’(–4, –1), S’(–1, 2), T’(3, 3)
2. 180° R’(1, –4), S’(–2, –1), T’(–3, 3)
3. 270° R’(4,1), S’(1, –2), T’(–3, –3)
Holt McDougal Geometry
9-3 Rotations
Classwork/Homework
• 9.3 W/S
Holt McDougal Geometry