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Exploring Transformations: Translation, Reflection, Rotation, and Dilations

Dive into the world of transformations with translations, reflections, rotations, and dilations. Understand pre-images, images, and how shapes change based on specific directions.

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Exploring Transformations: Translation, Reflection, Rotation, and Dilations

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  1. Transformations –Translation, Reflection, Rotation and Dilations

  2. Unit 4 –Transformations Transformations: It includes a change in a specific directions of a pre-image. These include translations, reflections, rotations, and dilations. Pre-image: The position of the shape before the change is made. Image: The position of the shape after the change is made. Translation: A transformation that “slides” a shape to another location. No change in size or angle of the shape.

  3. 4-1 Translations: You “slide” a shape up, down, right, left or all the above. Let’s see translation using a vector. Notation:(x, y) ( x + 5, y - 1) 5 units to the right and 1 unit down

  4. Transformation (x, y) (x + 5, y + 0) y A A’ B B’ C C’ x Pre-image A (-2, 4) B (-3, 2) C (-1, 1) Image A’ (3, 4) B’ (2, 2) C’ (4, 1)

  5. Transformation (x, y) (x - 3, y + 0) y A’ A B’ B C C’ x Pre-image A (-2, 4) B (-3, 2) C (-1, 1) Image A’ (-5, 4) B’ (-6, 2) C’ (-4, 1)

  6. Transformation (x, y) (x + 0, y - 5) y A B C x A’ Pre-image A (-2, 4) B (-3, 2) C (-1, 1) Image A’ (-2, -1) B’ (-3, -3) C’ (-1, -4) B’ C’

  7. Transformation (x, y) (x + 0, y + 4) y A’ B’ C’ A B C x Pre-image A (-2, 4) B (-3, 2) C (-1, 1) Image A’ (-2, 8) B’ (-3, 6) C’ (-1, 5)

  8. Transformation (x, y) (x + 3, y - 4) y A B C A’ x B’ Pre-image A (-2, 4) B (-3, 2) C (-1, 1) Image A’ (1, 0) B’ (0, -2) C’ (2, -3) C’

  9. Transformation (x, y) (x + 5, y + 2) y A’ A B’ C’ B C x Pre-image A (-2, 4) B (-3, 2) C (-1, 1) Image A’ (3, 6) B’ (2, 4) C’ (4, 3)

  10. Transformation (x, y) (x - 4, y - 5) y A B C x A’ Pre-image A (-2, 4) B (-3, 2) C (-1, 1) Image A’ (-6, -1) B’ (-7, -3) C’ (-5, -4) B’ C’

  11. Transformation (x, y) (x - 2, y + 3) y A’ B’ A C’ B C x Pre-image A (-2, 4) B (-3, 2) C (-1, 1) Image A’ (-4, 7) B’ (-5, 5) C’ (-3, 4)

  12. CW 4-1: Q# 5,6,9,10,11,12,13,14,17,18

  13. Answers

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