9-3 Rotations
You identified rotations and verified them as
congruence transformations.
• Draw rotations.
• Draw rotations in the coordinate plane.
How Many Degrees…
…are in a half turn?
180°
…are in a quarter turn?
90°
…three quarters turn?
270°
Definition
A rotation is a transformation that turns a set of
points about one point, the center of rotation.
The pre-image and image of any point are the
same distance from the center of rotation.
P (Pre-image)
Q
Center of
rotation
45° Angle of rotation
P’ (Image)
Definition continued
The angle of rotation measures how much a point
is turned about the center. For example, if point
P is rotated 45° clockwise about center of
rotation Q,
mPQP '  45
P (Pre-image)
Q
Center of
rotation
45° Angle of rotation
P’ (Image)
p. 640
Draw a Rotation
Rotate quadrilateral RSTV 45°
counterclockwise about point A.
• Draw a segment from point R to
point A.
• Use a protractor to measure a
45° angle counterclockwise with
as one side. Extend the other
side to be longer than AR.
• Locate point R' so that AR = AR'.
• Repeat this process for points S,
T, and V.
• Connect the four points to form
R'S'T'V'.
Quadrilateral R'S'T'V' is the image of
quadrilateral RSTV under a 45°
counterclockwise rotation about point A.
Answer:
For the diagram, which
description best identifies the
rotation of triangle ABC around
point Q?
A. 20° clockwise
B. 20° counterclockwise
C. 90° clockwise
D. 90° counterclockwise
When a point is rotated 90°, 180°, or 270°
counterclockwise around (0,0), you can use these rules:
p. 641
Spin It
When will the image
exactly overlap the
pre-image?
30° clockwise
60°clockwise
90°clockwise
120°clockwise
If a figure can be rotated onto itself with an angle
or rotation between 0° and 360 °, the figure has
rotational symmetry.
Rotations in the Coordinate Plane
Triangle DEF has vertices D(–2, –1),
E(–1, 1), and F(1, –1). Graph ΔDEF
and its image after a rotation of 115°
clockwise about the point G(–4, –2).
First, draw ΔDEF and plot point G.
Draw a segment from point G to
point D.
Use a protractor to measure a 115°
angle clockwise with
as one side.
Draw
Use a compass to copy
onto
Name the segment
Repeat with points E and F.
ΔD'E'F' is the image of ΔDEF
under a 115° clockwise
rotation about point G.
Answer:
Triangle ABC has vertices A(1, –2), B(4, –6), and
C(1, –6). Draw the image of ΔABC under a rotation of
70° counterclockwise about the point M(–1, –1).
A.
B.
C.
D.