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Geometry Transformations: Reflections, Rotations, and Translations

Learn about the different types of transformations in geometry, including reflections, rotations, and translations. Practice identifying and drawing reflections. Homework: Bring in a picture that shows a reflection.

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Geometry Transformations: Reflections, Rotations, and Translations

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  1. DRILL • If A is in between points B and C and AC is 4x + 12 and AB is 3x – 4 and BC is 57 feet how long is AB? • Angles A and B are Supplementary if Angle A is 2x – 20 and Angle B is 4x – 44. Find the measure of Angle A.

  2. Transformations • A transformation is any type of movement in geometry, it can be a change in shape, size, or simply location of an object. • The three types of Transformations we will talk about today are Reflections, Rotations and Translations.

  3. Pre-Image And Image • Pre-Image is the original figure before any type of transformation takes place. • Image is the new figure after the transformation has taken place.

  4. DO YOU SEE MATH IN THIS PICTURE?

  5. What about this one?

  6. How about now?

  7. Vocabulary Isometry: a transformation in which the original figure and it’s image are congruent. Opposite Orientation: when an image appears to be backwards compared to the pre-image.

  8. Reflection • A transformation in which a line of reflection acts as a mirror reflecting points from their pre-image to their image.

  9. Reflections • A reflection reverses orientation. • A reflection is an isometry. • A reflection over the x-axis results in a change in the y-coordinate. • A reflection in the y-axis results in a change in the x-coordinate.

  10. IS IT SYMMETRICAL? Directions • Take your paper, fold it so there are 4 sections. • Label each with Horizontal ONLY, Vertical ONLY, Both H &V, and/or Rotational

  11. Which category does it fit? • Directions: Draw each picture under the correct type of symmetry.

  12. Which category does it fit?

  13. Which category does it fit?

  14. Which category does it fit?

  15. An isometry is a transformation that does not change the shape or size of a figure. Reflections, translations, and rotations are all isometries. Isometries are also called congruence transformations or rigid motions. Recall that a reflection is a transformation that moves a figure (the preimage) by flipping it across a line. The reflected figure is called the image. A reflection is an isometry, so the image is always congruent to the preimage.

  16. Patty Paper Reflection • Fold patty paper both ways, so that you have 4 boxes. Darken the folds and label the x and y axes. • Draw any TRIANGLE in the 2nd Quadrant

  17. Reflection • Reflect your triangle over the x-axis. • What are the new coordinates?

  18. Reflection • Reflect your original triangle over the y-axis • What are the new coordinates?

  19. Reflection • Reflect your original over the line y=x. • What are the new coordinates?

  20. Conclusion • What can we conclude about coordinates and reflections? • Over the X-axis? • Over the Y-axis? • Over the line y = x?

  21. Rotational Symmetry • Wind Mill • How many degrees can each rotate?

  22. Class work • Complete reflection in the coordinate plane handout

  23. Wrap Up • Objective: SWBAT identify and draw reflections. • When asked to reflect this graph over the y-axis, this is the graph that was given. Is the student correct?

  24. Complete Exit TicketHomework:Bring in a picture that shows a reflection.

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