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Geometric Transformations

Geometric Transformations. by D. Fisher. Learning Targets. I can draw transformations of reflections, rotations, translations and combinations of these using graph paper, transparencies, and /or geometry software. Key Questions. What is a transformation? What is a pre-image?

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Geometric Transformations

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  1. Geometric Transformations by D. Fisher

  2. Learning Targets I can draw transformations of reflections, rotations, translations and combinations of these using graph paper, transparencies, and /or geometry software.

  3. Key Questions • What is a transformation? • What is a pre-image? • What is an image?

  4. Image – is the new figure. Image after the transformations. • Preimage – the original figure. Image before the transformations.

  5. Transformation • Transformation – In a plane, a mapping for which each point has exactly one image point and each image point has exactly one preimage point. • Reflection - A transformation representing a flip of a figure over a point, line, or plane.

  6. Rotation • Rotation - A transformation that turns every point of a preimage through a specified angle and direction about a fixed point, called the center of rotation. Rotate. • Translation – A transformation that moves all points of a figure the same distance in the same direction. A slide.

  7. 1. Reflection, Rotation, or Translation Rotation

  8. 2. Reflection, Rotation, or Translation Reflection

  9. 3. Reflection, Rotation, or Translation Translation

  10. 4. Reflection, Rotation, or Translation Reflection

  11. 5. Reflection, Rotation, or Translation Rotation

  12. 6. Reflection, Rotation, or Translation Translation

  13. 7. Reflection, Rotation, or Translation Reflection

  14. 8. Reflection, Rotation, or Translation Translation

  15. 9. Reflection, Rotation, or Translation Rotation

  16. 10. Why is this not perfect reflection? This is not a perfect reflection because the zebras have slightly different striping. One has its nose closer to the ground.

  17. 11. Reflection, Rotation, or Translation Translation

  18. 12. Reflection, Rotation, or Translation Reflection and rotation of 180o.

  19. 13. Reflection, Rotation, or Translation Rotation

  20. 14. Reflection, Rotation, or Translation Reflection in several directions.

  21. 15. Reflection, Rotation, or Translation Rotation

  22. 16. Reflection, Rotation, or Translation Reflection. Note the position of the purple tips; rotation of 180o would cause the top purple tip to be on the bottom.

  23. 17. Reflection, Rotation, or Translation Translation

  24. Reflection, Rotation, or Translation 18. Reflection in multiple mirrors

  25. 19. Reflection, Rotation, or Translation Translation. Watch the colors.

  26. 20. Reflection, Rotation, or Translation Reflection. Note the position of the red parts.

  27. 21. Reflection, Rotation, or Translation Rotation. Note the red parts.

  28. 22. The End The top left and the bottom right are reflections; the top right and the two on the bottom are rotations.

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