1. by D. Fisher Geometric Transformations

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. Reflection, Rotation, or Translation 1. Rotation

8. Reflection, Rotation, or Translation 2. Reflection

9. Reflection, Rotation, or Translation 3. Translation

10. Reflection, Rotation, or Translation 4. Reflection

11. Reflection, Rotation, or Translation 5. Rotation

12. Reflection, Rotation, or Translation 6. Translation

13. Reflection, Rotation, or Translation 7. Reflection

14. Reflection, Rotation, or Translation 8. Translation

15. Reflection, Rotation, or Translation 9. Rotation

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

17. Reflection, Rotation, or Translation 11. Translation

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

19. Reflection, Rotation, or Translation 13. Rotation

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

21. Reflection, Rotation, or Translation 15. Rotation

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

23. Reflection, Rotation, or Translation 17. Translation

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

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

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

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

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