section 7.2 rigid motion in a plane reflection. bell work 1.describe the translation in words:...
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Section 7.2
Rigid Motion in a PlaneReflection
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Bell Work1. Describe the translation in words:2. Write the translation in arrow notation:3. Write coordinates of both polygons:
A ( , ) A’( , )⤍B ( , ) B’( , )⤍C ( , ) C’( , )⤍D ( , ) D’( , )⤍E ( , ) E’ ( , )⤍
AB
CD
E
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Outcomes
• You will be able to identify what is a transformation and what is a reflection.
• You will be able to reflect a polygon on a coordinate grid across the x or y axis.
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TransformationsA transformation is a change in the __size_,
_location_, or _orientation_ of a figure.
• An Isometry is a transformation that preserves length, angle measures, parallel lines, and distances between points.
• Transformations that are isometries are called Rigid Motion Transformations.
Isometry
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Rigid Motion TransformationsThere are three kinds of rigid motion
transformations:
– Rotation – a “swing” around a point
– Reflection – a “flip” over a line
– Translation - a slide in one direction
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Reflection
• A reflection is a transformation which flips a figure over a line .
• This line is called the line of reflection.• A Reflection is an isometry.
A’
B C C’
A
B’
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Reflections
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ReflectionsTheorem 7.1 Reflection Theorem – A reflection is an isometry.
Write in - All points in a reflection are moved along lines that are perpendicular to the line of reflection.
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Reflections• Reflections and Line Symmetry• A figure in a plane has a line of symmetry if the
figure can be mapped onto itself by a reflection in that line.
• Different shapes have different lines of symmetry.
# of lines of symmetry?
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ReflectionExample 1: ΔABC is being reflected over the x-axis. Draw and label the image ΔA’B’C’.
What are the coordinates of :
A ( , ) ⤍ A’( , ) B( , ) ⤍ B’( , )C( , ) ⤍ C’( , )
A reflection can be written as ΔABC ⤍ ΔA’B’C’A
B
C
A general rule for an x-axis reflection:(x, y) ⤍ (x, -y)
This transformation is an isometry and so the image is congruent to the original.
A’C’
B’
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ReflectionExample 2: ΔABC is being reflected over the y-axis. Draw and label the image ΔA’B’C’.
What are the coordinates of :
A ( , ) ⤍ A’( , ) B( , ) ⤍ B’( , )C( , ) ⤍ C’( , )
A reflection can be written as ΔABC ⤍ ΔA’B’C’A
B
C
A general rule for a y-axis reflection:(x, y) ⤍ (-x, y)
This transformation is an isometry and so the image is congruent to the original.
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ReflectionExample 3: ΔJKL which has the coordinates
J(0, 2), K(3,4), and L(5, 1).Reflect in the x-axis and then the y-axis.
Write coordinates of : J( , ) J’( , ) J’’( , ) ⟶ ⟶K( , ) K’( , ) K’’( , )⟶ ⟶L( , ) L’( , ) ⟶ ⟶ L’’( , )Describe a different combination of two reflections that would move ΔJKL to ΔJ’’K’’L’’.
Is the last image congruent to the preimage?
K’’
K
K’
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Practice
Example 3: Write the rule…• When reflecting over the x-axis:
(x, y) ⤍ ( x, y)• When reflecting over the y-axis: (x, y) ⤍ ( x, y)
-
-
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PracticeExample 4&5: A(0,1), B(3,4), C(5,1)
What are the coordinates of ΔA’B’C’ if reflected in line x = -1?
A ( 0, 1) ⤍ A’( , ) B( 3 , 4 ) ⤍ B’( , )C( 5 , 1) ⤍ C’( , )
What are the coordinates of A’B’C’ if reflected in line y = -2?
A( , ) ⤍ A’( , ) B( , ) ⤍ B’( , )C( , ) ⤍ C’( , )
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Reflection
x = 0Or the y-axis
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Reflection
y = -1
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Reflection and Translation• Example 8: Quadrilateral CDEF is plotted on the grid below. • On the graph, draw the reflection of polygon CDEF over the x-axis.
Label the image C’D’E’F’.• Now create polygon C”D”E”F” by translating polygon C’D’E’F’ three
units to the left and up two units. What will be the coordinates of point C”?
C’’(-3,0)
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• Don’t forget about your IP in the textbook!