Transcript Document

Lesson 9-3
Rotations
or
Turns
5-Minute Check on Lesson 9-2
Transparency 9-3
Find the coordinates of each figure under the given translation.
1. RS with endpoints R(1,-3) and S(-3,2) under the
translation right 2 units and down 1 unit.
R’(3,-4), S’(-1,1)
2. Quadrilateral GHIJ with G(2,2), H(1,-1), I(-2,-2), and J(-2,5) under the
translation left 2 units and down 3 units. G’(-1,0), H’(-2,-3),
3. ∆ABC with vertices A(-4,3), B(-2,1), and C(0,5) under I’(-5,-4), J’(-5,3)
the translation (x, y)  (x + 3, y – 4) A’(-1,-1), B’(1,-3), C’(3,1)
4. Trapezoid LMNO with vertices L(2,1), M(5,1), N(1,-5), and O(0-2)
under the translation (x, y)  (x – 1, y + 4) L’(1,5), M’(4,5), N’(0,-1),
5. Find the translation that moves AB with endpoints O’(-1,2)
A(2,4) and B(-1,-3) to A’B’ with endpoints A’(5,2) and B’(2,-5)
6. Standardized Test Practice: Which describes (x, y)  (x + 3, y – 2)
the translation left 3 units and up 4 units?
A
(x, y)  (x + 3, y – 4)
B
(x, y)  (x – 3, y – 4)
C
(x, y)  (x + 3, y + 4)
D
(x, y)  (x – 3, y + 4)
Click the mouse button or press the
Space Bar to display the answers.
Objectives
• Draw rotated images using the angle of
rotation
• Identify figures with rotational symmetry
Vocabulary
• Rotation – transformation that turns every point of a
pre-image through a specified angle and direction
about a fixed point
• Center of rotation – fixed point of the rotation
• Angle of rotation – angle between a pre-image point
and corresponding image point
• Rotational symmetry – a figure can be rotated less
than 360° so that the pre-image and image look the
same (indistinguishable)
– Order – number of times figure can be rotated less than 360°
in above
– Magnitude – angle of rotation (360° / order)
Triangle DEF has vertices D(–2, –1), E(–1, 1), and
F(1, –1). Draw the image of DEF under a rotation of
115° clockwise about the point G(–4, –2).
First draw DEF 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.
E
D
F
G
115
D'
E'
F'
R
D'E'F' is the image of DEF under a 115° clockwise
rotation about point G.
Answer:
E
D
F
D'
E'
F'
Triangle ABC has vertices A(1, –2), B(4, –6), and
C(1, –6). Draw the image of ABC under a rotation of
70° counterclockwise about the point M(–1, –1).
Answer:
Find the image of parallelogram WXYZ under
reflections in line p and then line q.
First reflect parallelogram
WXYZ in line p. Then label the
image W'X'Y'Z'.
Next, reflect the image in line q.
Then label the image W''X''Y''Z''.
Answer:
Parallelogram W''X''Y''Z'' is the
image of parallelogram WXYZ
under reflections in line p and q.
Find the image of ABC under reflections in line m and
then line n.
Answer:
Rotation
Rotation – a transformation that turns all points of a figure, through a
specified angle and direction about a fixed point
y
B’
A (2,7)
B (8,4)
C (3,3)
A
B
C’
A’
C
x
Each point rotated
90° to the left
(counter clockwise)
around the origin
point of rotation
(origin)
angle of rotation
(90°)
In Powerpoint:
the free rotate
(green dot) allows
rotation, but only
around the figure’s
center point – not
an outside point
180° Rotation – reflection across the origin!
QUILTS Use the quilt by Judy Mathieson shown below.
Identify the order and magnitude of the symmetry in
the medium star directly to the left of the large star in
the center of the quilt.
Answer: The medium star
directly to the left of
the large star in the
center has rotational
symmetry of order 16
and a magnitude of
22.5°.
QUILTS Use the quilt by Judy Mathieson shown below.
Identify the order and magnitude of the symmetry in
the tiny star above the medium-sized star in
Example 3a.
Answer: The tiny star has
rotational symmetry
of order 8 and
magnitude of 45°.
QUILTS Use the quilt by Judy Mathieson shown below.
Identify the order and magnitude of the symmetry in
each part of the quilt.
a. star in the upper left corner
Answer: 8; 45°
b. medium-sized star
directly in center of quilt
Answer: 20; 18°
Rotational Symmetry
Rotational Symmetry – if a figure can be rotated less than
360° and the image and pre-image are indistinguishable
(regular polygons are a great example)
Order:
3
4
6
8
Magnitude:
120°
90°
60°
45°
Remember Order = n (number of sides) and Magnitude = 360 / Order
Summary & Homework
• Summary:
– A rotation turns each point in a figure through the
same angle about a fixed point
– An object has rotational symmetry when you can
rotate it less than 360° and the pre-image and the
image are indistinguishable (can’t tell them apart)
• Homework:
– pg 479-481; 9, 10, 14, 15, 23, 41