Basic Reflections and Translations

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What is a Transformation?

• Basic Reflections and Translations
• By Heather Blanchard

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A transformation is

• a correspondence between two sets of points where
  every point in the preimage has a unique image,
  and every point in the image has exactly one
  preimage
• the original object is called the preimage, and
  the object that has been transformed is called
  the image

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Here is an example of a transformation
B
A
B
A
C
D
D
C
preimage
image
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This type of transformation is called a
reflection.
B
A
B
A
C
D
D
C
preimage
image
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A reflection is a transformation that can be
thought of as a flip over a given line.
B
A
B
A
C
D
D
C
preimage
image
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Another type of transformation is a translation,
or slide. Here is an example of one.
A
A
B
C
B
C
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A translation is a transformation that moves each
point on the preimage the same length and
direction as a given vector.
A
A
B
C
vector
B
C
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Is this a reflection or a translation?

• Please take out a pencil and paper and follow
  along, or click this link to print an activity
  sheet.

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Is this a reflection or a translation?
10
Is this a reflection or a translation?
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Is this a reflection or a translation?
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All done? Great!

• Here are the answers

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The correct answers are
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Transformations Reflections and Translations
Try to figure out what kind of transformation
each of these objects have undergone. Circle the
correct answer for each.
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References

• The University of Chicago Mathematics Project.
  Geometry. Upper Sadle River, NJ Prentice-Hall,
  Inc., 2002.
• MSN Learning and Research. 12 Nov. 2003.
  http//encarta.msn.com.
• Google Images. 22 Nov. 2003. http//www.google.co
  m/images.