1.6 Motions in Geometry

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1.6 Motions in Geometry
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Vocabulary
transformation translation rotation center of
rotation reflection preimage image glide
reflection dilation
Homework
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Translations, rotations, and reflections are type
of transformations.
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A transformation is an operation that changes
some aspect of the geometric figure to produce a
new figure. The new figure is called the image,
and the original figure is called the pre-image.
The resulting figure of a translation, glide
reflection, rotation or reflection is congruent
to the original figure.
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A dilation is a transformation an operation
that changes the size of a figure. The resulting
figure of a dilation is similar to the original
figure.
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A special type of composition of
transformations starts with a translation
followed by a reflection. This is called a glide
reflection.
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Reflection, Rotation, or Translation
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Reflection, Rotation, or Translation
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Reflection, Rotation, or Translation
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Glide Reflection
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Translation
Preimage
A
C
Slide Arrow
B
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Rotation 90 180 270
Image 270?
Image 90?
Image 180?
Clockwise Rotation
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Reflection
Preimage
Image
Line of reflection
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Complete the figure. The dashed line is the line
of symmetry.
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Complete the figure. The dashed line is the line
of symmetry.
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Complete the figure. The dashed line is the line
of symmetry.
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Complete the figure. The dashed line is the line
of symmetry.
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Complete the figure. The point is the center of
rotation.
10-fold
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Draw a reflection of ?ABC across line of
reflection m.
STEP 1
Find the distance from B to line m (distance is
perpendicular).
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Draw a reflection of ?ABC across line of
reflection m.
STEP 4
STEP 3
Label point B'. Erase All other lines.
Repeat Steps 1 3 for each vertex. Draw
?A'B'C'.
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FOUR CASES OF REFLECTION
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Draw a reflection of ?ABC along line m.
STEP 1
Find the distance from B to line m (distance is
perpendicular).
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Draw a reflection of ?ABC across line of
reflection m.
STEP 4
Repeat Steps 1 3 for each vertex. Draw
?A'B'C'.
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AssignmentSection 11 - 28