Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up
1. Subtract 3 from the x-coordinate and 2 from
the y-coordinate in (7, 4).
(4, 6)
(12, 27)
2. Multiply each coordinate by 3 in (4, 9).
3. Subtract 4 from the x-coordinate and add 3 to
the to the y-coordinate in (2, 1).
(6, 2)
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Problem of the Day Some numbers appear as
different numbers when rotated or reflected. Name
as many as you can.
Possible answers 6 and 9 6999 and 6669 IV and
VI IX and XI
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Learn to recognize, describe, and show
transformations.
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Insert Lesson Title Here
Vocabulary
transformation image translation reflection line
of reflection rotation
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In mathematics, a transformation changes the
position or orientation of a figure. The
resulting figure is the image of the original.
Images resulting from the transformations
described in the next slides are congruent to the
original figures.
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Types of Transformations
Translation The figure slides along a straight
line without turning.
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Types of Transformations
Reflection The figure flips across a line of
reflection, creating a mirror image.
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Types of Transformations
Rotation The figure turns around a fixed point.
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Additional Example 1 Identifying Types of
Transformations
Identify each type of transformation.
B.
A.
The figure flips across the y-axis.
The figure slides along a straight line.
It is a translation.
It is a reflection.
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Check It Out Example 1
Identify each type of transformation. A.
B.
4
4
2
2
4
4
0
4
4
0
2
2
2
2
2
2
4
4
The figure slides along a straight line.
The figure turns around a fixed point.
It is a translation.
It is a rotation.
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Additional Example 2 Graphing Transformations on
a Coordinate Plane
Graph the translation of quadrilateral ABCD 4
units left and 2 units down.
Each vertex is moved 4 units left and 2 units
down.
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Reading Math
A is read A prime and is used to represent the
point on the image that corresponds to point A of
the original figure
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Check It Out Example 2
Translate quadrilateral ABCD 5 units left and 3
units down.
B
A
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Each vertex is moved five units left and three
units down.
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C
D
4
2
4
2
2
4
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Additional Example 3 Graphing Reflections on a
Coordinate Plane
Graph the reflection of the figure across the
indicated axis. Write the coordinates of the
vertices of the image. x-axis, then y-axis
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Additional Example 3 Continued
A. x-axis.
The x-coordinates of the corresponding vertices
are the same, and the y-coordinates of the
corresponding vertices are opposites.
The coordinates of the vertices of triangle ADC
are A(3, 1), D(0, 0), C(2, 2).
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Additional Example 3 Continued
B. y-axis.
The y-coordinates of the corresponding vertices
are the same, and the x-coordinates of the
corresponding vertices are opposites.
The coordinates of the vertices of triangle ADC
are A(3, 1), D(0, 0), C(2, 2).
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Insert Lesson Title Here
Check It Out Example 3A
Graph the reflection of the triangle ABC across
the x-axis. Write the coordinates of the vertices
of the image.
The x-coordinates of the corresponding vertices
are the same, and the y-coordinates of the
corresponding vertices are opposites.
B
3
C
A
3
The coordinates of the vertices of triangle ABC
are A(1, 0), B(3, 3), C(5, 0).
3
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Check It Out Example 3B
Graph the reflection of the triangle ABC across
the y-axis. Write the coordinates of the vertices
of the image.
The y-coordinates of the corresponding vertices
are the same, and the x-coordinates of the
corresponding vertices are opposites.
A
The coordinates of the vertices of triangle ABC
are A(0, 0), B(2, 3), C(2, 3).
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Additional Example 4 Graphing Rotations on a
Coordinate Plane
Triangle ABC has vertices A(1, 0), B(3, 3), C(5,
0). Rotate ?ABC 180 about the vertex A.
Notice that vertex C is 4 units to the right of
vertex A, and vertex C is 4 units to the left of
vertex A.
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Check It Out Example 4
Triangle ABC has vertices A(0, 2), B(0, 3),
C(0, 3). Rotate ?ABC 180 about the vertex A.
B
3
A
Notice that vertex B is 2 units to the right and
3 units above vertex A, and vertex B is 2 units
to the left and 3 units below vertex A.
3
3
C
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Insert Lesson Title Here
Lesson Quiz Part I
reflection
1. Identify the transformation.
2. The figure formed by (5, 6), (1, 6), and
(3, 2) is transformed 6 units right and 2
units up. What are the coordinates of the new
figure?
(1, 4), (5, 4), (9, 4)
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Insert Lesson Title Here
Lesson Quiz Part II
3. Graph the triangle with vertices A(1, 0),
B(3, 0), C(1, 4). Rotate ?ABC 90
counterclockwise around vertex B and reflect the
resulting image across the y-axis.
C
A
B