Geometric Transformations

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Presentation transcript:

Geometric Transformations Please send feedback to fisher_d@madera.k12.ca.us Answers and discussion are in the notes for each slide. 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? What is an image?

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

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.

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.

Reflection, Rotation, or Translation 1. Reflection, Rotation, or Translation Rotation Rotation

Reflection, Rotation, or Translation 2. Reflection, Rotation, or Translation Reflection Reflection

Reflection, Rotation, or Translation 3. Reflection, Rotation, or Translation Translation Translation

Reflection, Rotation, or Translation 4. Reflection, Rotation, or Translation Reflection Reflection

Reflection, Rotation, or Translation 5. Reflection, Rotation, or Translation Rotation Rotation

Reflection, Rotation, or Translation 6. Reflection, Rotation, or Translation Translation Translation

Reflection, Rotation, or Translation 7. Reflection, Rotation, or Translation Reflection Reflection

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

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

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.

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

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

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

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

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

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.

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

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

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

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.

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

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.