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Transformations

Transformations. transformation. A change of position or size of a figure. Translations Reflections Rotations Dilation. 4 types:. translation. A transformation that moves points the same distance and in the same direction. * The figures are congruent!. * The original image is slid!.

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Transformations

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  1. Transformations

  2. transformation • A change of position or size of a figure. • Translations • Reflections • Rotations • Dilation 4 types:

  3. translation • A transformation that moves points the same distance and in the same direction. * The figures are congruent! * The original image is slid!

  4. Example:

  5. reflections • The mirror image of the original figure * The figures are congruent! * The original image is flipped!

  6. Line of Reflection Example:

  7. The line of Reflection is also called the line of symmetry.

  8. It is also possible to have a reflection image with respect to a point.

  9. Point of Symmetry • The point must be the midpoint for all segments that pass through it and have endpoints on the figure.

  10. A T M H Example Does Rhombus MATH have point symmetry? Yes

  11. Fixed point rotation • A transformation that turns a figure about a fixed point. Example:

  12. Another Example:

  13. Dilation • Change in size of a figure • Enlarge or shrink • Similar figures (congruent angles, proportional side lengths)

  14. Original Figure

  15. isometry • Congruence Transformation • Maps every segment to a congruent segment • No change in size! • Congruent sides and congruent angles

  16. State whether each of the following have isometry. • Translation • Reflection • Rotation • Dilation Yes Yes Yes No

  17. Transformationsare used to make tessellations

  18. tessellation • A repeating pattern of figures that completely covers a plane without gaps or overlaps.

  19. Transformationsin the work ofM.C. Escher

  20. Learn more about M.C. Escher • http://www.mcescher.com/

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