1. Geometric Transformations
Please send feedback to Answers and discussion are in the notes for each slide.
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. Preimage – Image – is the new figure. Image after the transformations.
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 Translation1.
Reflection, Rotation, or Translation
Rotation
Rotation

8. Reflection, Rotation, or Translation2.
Reflection, Rotation, or Translation
Reflection
Reflection

9. Reflection, Rotation, or Translation3.
Reflection, Rotation, or Translation
Translation
Translation

10. Reflection, Rotation, or Translation4.
Reflection, Rotation, or Translation
Reflection
Reflection

11. Reflection, Rotation, or Translation5.
Reflection, Rotation, or Translation
Rotation
Rotation

12. Reflection, Rotation, or Translation6.
Reflection, Rotation, or Translation
Translation
Translation

13. Reflection, Rotation, or Translation7.
Reflection, Rotation, or Translation
Reflection
Reflection

14. Reflection, Rotation, or Translation8.
Reflection, Rotation, or Translation
Translation
Translation

15. Reflection, Rotation, or Translation9.
Reflection, Rotation, or Translation
Rotation
Rotation

16. Why is this not perfect reflection?
10.
Why is this not perfect reflection?
The zebras have slightly different striping. One has its nose closer to the ground.
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.
Reflection, Rotation, or Translation
Translation.
Translation

18. Reflection, Rotation, or Translation
12.
Reflection, Rotation, or Translation
Reflection. However, rotation of 180o will be the same.
Reflection and rotation of 180o.

19. Reflection, Rotation, or Translation
13.
Reflection, Rotation, or Translation
Rotation
Rotation

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

21. Reflection, Rotation, or Translation
15.
Reflection, Rotation, or Translation
Rotation
Rotation

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

23. Reflection, Rotation, or Translation
17.
Reflection, Rotation, or Translation
Translation.
Translation

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

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

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

27. Reflection, Rotation, or Translation
21.
Reflection, Rotation, or Translation
Rotation. Note the red parts.
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.
The top left and the bottom right are reflections; the top right and the two on the bottom are rotations.