Geometry Transformations

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Geometry Transformations

• The Basics

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Basic Definitions click to see a concept map

• Translation
• Rotation
• Reflection
• Glide Reflection
• Dilation
• Isometry

Click on the word to go to the definition
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Translation

• A transformation that moves points the same
  distance and in the same direction
• It is an isometry
• A composition of reflections in two parallel
  lines.

Back to definitions
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Rotations

• An image is turned about a point, where all
  points are x from that point.
• It is an isometry.
• A composition of reflections in two intersecting
  lines is a rotation.

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Reflections

• When you fold the object on a line and the same
  object appears
• It is an isometry

?ABC is reflected about the y-axis
Back to definitions
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Glide Reflections

• It is a composition of a translation and a
  reflection
• It is an isometry.

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Dilation

• Has a center and a scale factor.
• Enlargement- image is larger than the original
• Reduction- image is smaller than the original
  figure.

This is an enlargement.
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Isometry

• Original figure and its image (transformed
  figure) are congruent (same size and shape).
• Translation, Rotation, Reflection, and Glide
  Reflection are isometries.

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A Famous Person

• Who uses transformations in his work!!!

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Biography M.C. Escher

• Maurits Cornelis Escher (1898-1972)
• Click to see a Database of M.C. Escher.
• He made 448 lithographs, woodcuts and wood
  engravings and over 2000 drawings and sketches
• Born in Leeuwarden
• His wife Jetta Umiker, whom he married in 1924.
  They settled in Rome, where they stayed until
  1935.

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M.C. Escher

• Here is a Video of M.C. Escher
• His art contains many types of transformations.
• His website is http//www.mcescher.com
• Pictures of his containing transformations.

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M.C. Escher Reflection

• Fold on the diagonal

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M.C. Escher Translation

• The fish and bird are a translation

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M.C. Escher Rotation

• The stairs are a rotation

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The End