Translations.

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Transformations on the Coordinate Plane

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Presentation transcript:

Translations

Definitions: Transformation: A change in a shape’s size or position. 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.

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

Transformation (x, y) (x + 5, y + 0) Pre-image A (-2, 4) A’ (3, 4) 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)

Transformation (x, y) (x - 3, y + 0) Pre-image A (-2, 4) A’ (-5, 4) 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)

Transformation (x, y) (x + 0, y - 5) Pre-image Image A (-2, 4) 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’

Transformation (x, y) (x + 0, y + 4) Pre-image A (-2, 4) A’ (-2, 8) 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)

Transformation (x, y) (x + 3, y - 4) Pre-image Image A (-2, 4) 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’

Transformation (x, y) (x + 5, y + 2) Pre-image Image A (-2, 4) 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)

Transformation (x, y) (x - 4, y - 5) Pre-image A (-2, 4) A’ (-6, -1) 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’

Transformation (x, y) (x - 2, y + 3) Pre-image A (-2, 4) A’ (-4, 7) 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)

In-class Translation Project!

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