do now (4, –6) (12, 27) (–6, 2) course 2 8-10 translations, reflections, and rotations 1....
TRANSCRIPT
Do Now
(4, –6)(12, 27)
(–6, 2)
Course 2
8-10 Translations, Reflections, and Rotations
1. Subtract 3 from the x-coordinate and 2 from the y-coordinate in (7, –4).
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).
Hwk: p 77 #1-4
GEORGIA PERFORMANCE STANDARDS:M7G2.a Demonstrate understanding of translations, dilations, rotations, reflections, and relate symmetry toappropriate transformations; M7G2.b Given a figure in the coordinate plane, determine the coordinates resultingfrom a translation, dilation, rotation, or reflection
EQ: How do I recognize, describe, and show transformations?
Vocabulary
transformationimagetranslationreflectionline of reflectionrotation
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Course 2
8-10 Translations, Reflections, and Rotations
VocabularyTransformation- changes the position or orientation of a figureImage- resulting figure Translation- slides without turning Reflection- flips across a line of reflection line of reflection- x or y axis Rotation- turns around a fixed pointDilation- make bigger or smaller
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Course 2
8-10 Translations, Reflections, and Rotations
In mathematics, a transformationchanges the position or orientation of a figure. The resulting figure is the imageof the original. Images resulting fromthe transformations described in the next slides are congruent to the original figures.
Course 2
8-10 Translations, Reflections, and Rotations
TranslationThe figure slides along a straight line without turning.
Course 2
8-10 Translations, Reflections, and Rotations
Types of Transformations
ReflectionThe figure flips across a line of reflection, creating a mirror image.
Course 2
8-10 Translations, Reflections, and Rotations
Types of Transformations
RotationThe figure turns around a fixed point.
Course 2
8-10 Translations, Reflections, and Rotations
Types of Transformations
Identify each type of transformation.
Additional Example 1: Identifying Types of Transformations
The figure flips across the y-axis.
A. B.
It is a translation.Course 2
8-10 Translations, Reflections, and Rotations
It is a reflection.
The figure slides along a straight line.
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Course 2
8-10 Translations, Reflections, and Rotations
The point that a figure rotates around may be on the figure or away from the figure.
Helpful Hint
Check It Out: Example 1
Identify each type of transformation.
A. B.
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Course 2
8-10 Translations, Reflections, and Rotations
x
y
2
2
–2
–4
4
4
–4
–2 0
x
y
2
2
–2
–4
4
4
–4
–2 0
It is a translation.
The figure slides along a straight line.
It is a rotation.
The figure turns around a fixed point.
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.
Course 2
8-10 Translations, Reflections, and Rotations
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A’ is read “A prime” and is used to represent the point on the image that corresponds to point A of the original figure
Reading Math
Course 2
8-10 Translations, Reflections, and Rotations
Check It Out: Example 2
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Translate quadrilateral ABCD 5 units left and 3 units down.
Each vertex is moved five units left and three units down.
x
yA
B
C
2
2
–2
–4
4
4
–4
–2 D
D’C’
B’A’
Course 2
8-10 Translations, Reflections, and Rotations
Graph the reflection of the figure across the indicated axis. Write the coordinates of the vertices of the image.
x-axis, then y-axis
Additional Example 3: Graphing Reflections on a Coordinate Plane
Course 2
8-10 Translations, Reflections, and Rotations
A. x-axis.
Additional Example 3 Continued
The x-coordinates of the corresponding vertices are the same, and the y-coordinates of the corresponding vertices are opposites.
Course 2
8-10 Translations, Reflections, and Rotations
The coordinates of the vertices of triangle ADC are A’(–3, –1), D’(0, 0), C’(2, –2).
B. y-axis.
Additional Example 3 Continued
The y-coordinates of the corresponding vertices are the same, and the x-coordinates of the corresponding vertices are opposites.
Course 2
8-10 Translations, Reflections, and Rotations
The coordinates of the vertices of triangle ADC are A’(3, 1), D’(0, 0), C’(–2, 2).
Check It Out: Example 3A
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3
x
y
A
B
C
3
–3
Course 2
8-10 Translations, Reflections, and Rotations
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.
The coordinates of the vertices of triangle ABC are A’(1, 0), B’(3, –3), C’(5, 0).
A’
B’
C’
Check It Out: Example 3B
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A x
y
B
C
3
3
–3
Course 2
8-10 Translations, Reflections, and Rotations
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.
The coordinates of the vertices of triangle ABC are A’(0, 0), B’(–2, 3), C’(–2, –3).C’
B’
Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 180° about the vertex A.
Additional Example 4: Graphing Rotations on a Coordinate Plane
Course 2
8-10 Translations, Reflections, and Rotations
x
y
A
B
C
3
–3
The corresponding sides, AC and AC’ make a 180° angle.
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.
C’
B’
A’
Triangle ABC has vertices A(0, –2), B(0, 3), C(0, –3). Rotate ∆ABC 180° about the vertex A.
Check It Out: Example 4
Course 2
8-10 Translations, Reflections, and Rotations
The corresponding sides, AB and AB’ make a 180° angle.
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.
x
y
B
C
3
3
–3B’
C’
A
TOTD
1. Identify the transformation.
(1, –4), (5, –4), (9, 4)
reflection
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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?
Course 2
8-10 Translations, Reflections, and Rotations
TOTD
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.
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Course 2
8-10 Translations, Reflections, and Rotations
x
y
2
–2
2–2–4
–4
4
4
C
B AC’
B’
A’
C’’A’’
B’’