Understanding Transformations in Geometry

Discover the concept of transformations in geometry, including translations, rotations, reflections, and dilations. Learn about pre-image and image positions, notation for translations, and explore various transformation examples with visual representations.

• Geometry
• Transformations
• Translation
• Shapes
• Pre-image

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1. Translations

2. Definitions: Transformations: It is a change that occurs that maps or moves a shape in a specific directions onto an image. These are translations, rotations, reflections, 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.

3. Translations: You slide a shape up, down, right, left or all the above. Notation: (x, y) ( x + 2, y - 3)

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

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

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

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

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

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

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

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

12. In-class Translation Project!

13. Transformation y (x, y) (x + 6, y - 7) x