Chapter 9: Transformations 9.1 Translations

Review Coordinate Points How do I graph (-3,4)?? Which axis is x, which is y?

Transformations change in position, shape or size of a geometric figure uses coordinate plane geometry

Vocab pre-image: original figure image: the resulting figure after a transformation isometry: transformation in which the preimage and image are congruent

Example 1 Is this transformation an isometry?

Example 1 Is this transformation an isometry?

Example 1 Is this transformation an isometry?

Notation Transformations are named as follows: ΔABC → ΔA’B’C’

Example 2 In the diagram, E’F’G’H’ is an image of EFGH. Name the images of angle F and angle H. List all pairs of corresponding sides.

Translations called a “slide” maps all points of a figure the same distance in the same direction written as: (2,3) → (x + 4, y – 2)

Example 3 Find the image of ΔXYZ under the translation (x,y)→(x – 2, y – 5).

Example 3a Find the image of ΔXYZ under the translation (x,y)→(x – 4, y + 1).

Example 4 Write a rule to describe the translation PQRS→P’Q’R’S’

Example 4a The translation image of ΔLMN with vertices L(-6,-1), M(-4,-3), and N(-1,-1) is translated to L’(1,-2), M’(3,-4), and N’(6,-2). Write the rule to describe the translation.

Compositions combination of two or more transformations each transformation is performed on the image of the preceding transformation

Example 5 Yolanda is visiting San Francisco. From her hotel near Union Square, she walks 4 blocks east and 4 blocks north to the Wells Fargo History Museum to see a stagecoach and relics of the Gold Rush. Then she walks 5 blocks west and 3 blocks north to the Cable Car Barn Museum. Now how many blocks is she from her hotel?

Homework p. 473 7-18, 20, 22 (you need graph paper!!)