# Transformations

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```					Transformations

Chapter 7
January 2008
Definitions

 Image: A new figure that results from the
transformation of a figure in a plane.
 Preimage: The original image in the
transformation of a figure in a plane.
 Transformation: The operation that maps,
or moves, a preimage onto an image.
 Isometry: A transformation that preserves
lengths. Also known as rigid transformations.
Types of Transformations

 Translation: A transformation that maps
every point on the preimage the same distance
to the image.
 Reflection: A transformation that flips the
preimage across an axis onto the image (Like
a mirror would do to an image).
 Rotation: A transformation that rotates the
preimage around an angle onto the image.
Symbols
 The following symbol is used to show a
transformation. →
 ∆ABC → ∆DEF
 This means triangle ABC is transformed to
triangle DEF.
 What is the image?
 ∆DEF
 What is the preimage?
 ∆ABC
Transformations

 Think of it as dragging a figure to another
area.
Reflections

 Remember a mirror. The image is
reversed or flipped.
Rotations

 Think of a merry-go-round. The image is
What kind of
transformation is it?
What kind of
transformation is it?
What kind of
transformation is it?
Isometry

 A transformation that preserves length. Hence,
the size of the preimage is the same size as
the image. All corresponding parts are
congruent. The following reflection is an
isometry.
Is it an isometry?
 1.        2.


YES          NO
Examples
Examples

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