Course 3 Chapter 5 Lesson 7

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7-7
Transformations
Warm Up
Problem of the Day
Lesson Presentation
Course 3
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Warm Up
Determine if the following sets of points form a
parallelogram.
1. (3, 0), (1, 4), (6, 0), (2, 4)
yes
2. (1, 2), (2, 2), (2, 1), (1, 2)
no
3. (2, 3), (3, 1), (1, 4), (6, 2)
yes
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Problem of the Day How can you move just one
number to a different triangle to make the sum of
the numbers in each triangle equal? (Hint There
do not have to be exactly 3 numbers in each
triangle.)
Move the 9 to the first triangle.
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Learn to transform plane figures using
translations, rotations, and reflections.
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Vocabulary
transformation translation rotation center of
rotation reflection image
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When you are on an amusement park ride, you are
undergoing a transformation. Ferris wheels and
merry-go-rounds are rotations. Free fall rides
and water slides are translations. Translations,
rotations, and reflections are type of
transformations.
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The resulting figure or image, of a translation,
rotation or reflection is congruent to the
original figure.
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Additional Example 1 Identifying Transformations
Identify each as a translation, rotation,
reflection, or none of these.
B.
A.
rotation
reflection
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Additional Example 1 Identifying Transformations
Identify each as a translation, rotation,
reflection, or none of these.
C.
D.
none of the these
translation
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Check It Out Example 1
Identify each as a translation, rotation,
reflection, or none of these.
A.
B.
B
A
A
C
D
C
B
reflection
translation
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Check It Out Example 1
Identify each as a translation, rotation,
reflection, or none of these.
E
C.
D.
A
F
D
A
B
B
C
F
C
D
none of these
rotation
E
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Additional Example 2A Graphing Transformations
Draw the image of the triangle with vertices
A(1, 1), B(2, -2), and C(5, 0) after each
transformation. A 180 counterclockwise rotation
around (0, 0)
y
B
2
A
x
C
0
C
2
4
2
4
A
2
B
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Additional Example 2B Graphing Transformations
Draw the image of the triangle with vertices
A(1, 1), B(2, -2), and C(5, 0) after each
transformation. A reflection across the y-axis
y
2
A
A
x
C
0
C
2
4
2
4
2
B
B
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Check It Out Example 2A
Draw the image of the triangle with vertices
A(1, 2), B(2, 3), and Z(7, 0) after each
transformation. A 180 counterclockwise rotation
around (0, 0)
y
Y
X
2
x
0
Z
Z
2
4
2
4
2
X
Y
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Check It Out Example 2A
Draw the image of the triangle with vertices
A(1, 2), B(2, -3), and Z(7, 0) after each
transformation. A reflection across the y-axis
y
X
X
2
x
0
Z
Z
2
4
2
4
2
Y
Y
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Additional Example 3A Describing Graphs of
Transformations
Rectangle HIJK has vertices H(0, 2), I(4, 2),
J(4, 4), and K(0, 4). Find the coordinates of the
image of the indicated point after each
transformation.
y
Translation 2 t units up, point H
H(0, 4)
x
2
2
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Additional Example 3B Describing Graphs of
Transformations
Rectangle HIJK has vertices H(0, 2), I(4, 2),
J(4, 4), and K(0, 4). Find the coordinates of the
image of the indicated point after each
transformation.
y
90 rotation around (0, 0), point I
x
I(2, 4)
H
K
2
2
I
J
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Check It Out Example 3A
Parallelogram ABCD has vertices A(1, 2), B(3,
2), C(7, 3), and D(6, 1). Find the coordinates
of the images of the indicated point after each
transformation.
y
180 clockwise rotation around (0, 0), point A
2
x
2
A(1, 2)
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Check It Out Example 3B
Parallelogram ABCD has vertices A(1, 2), B(3,
2), C(7, 3), and D(6, 1). Find the coordinates
of the images of the indicated point after each
transformation.
y
Translation 10 units left, point C
2
x
C(-3, 3)
2
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Lesson Quiz Part I
Given the coordinates for the vertices of each
pair of quadrilaterals, determine whether each
pair represents a translation, rotation,
reflection, or none of these.
1. (2, 2), (4, 0), (3, 5), (6, 4) and (3,
1), (5, 3), (4, 2), (7, 1)
translation
2. (2, 3), (5, 5), (1, 2), (5, 4) and (2,
3), (5, 5), (1, 2), (5, 4)
reflection
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Lesson Quiz Part II
Given the coordinates for the vertices of each
pair of quadrilaterals, determine whether each
pair represents a translation, rotation,
reflection, or none of these.
3. (1, 3), (1, 2), (2, 3), (4, 0) and (1,
3), (1, 2), (2, 3), (4, 0)
none
4. (4, 1), (1, 2), (4, 5), (1, 5) and (4,
1), (1, 2), (4, 5), (1, 5)
rotation