1. Translations, Reflections, & Rotations
9.1, 9.2, & 9.3: Transformations --
Translations, Reflections, & Rotations
VIDEO!
Write the following definitions:
Transformation
Rotation
Translation
Reflection

2. Transformations
Transformation: A change in a figure’s position, shape, or size.

3. Translations
Translation: a “slide” that moves a point a certain distance in a certain direction
Ex1) Find the image of the point B(3, -4) after being translated left 5 and up 7.

4. Translations
Ex2) Given the transformation below, describe the translation.
Ex3) Write a rule to describe the translation PQRS P’Q’R’S’

5. Reflections Some Reflection Rules:
Reflection: a “flip” across a specified line
Some Reflection Rules:
**Original point and image are the same distance away from the line of reflection
Across x-axis: (x, y)  (-x, y)
Across y-axis: (x, y)  (x, -y)
Ex4) Find the image of L(-2, 5) after being reflected across the y-axis.

6. Reflections
Ex6) Given the points R(-2,-1), A(1,-3), D(-2,-3), draw ΔRAD and its reflection image across the line x = 2.

7. Rotations Rotation Rules (around the origin):
Rotation: a “turn” of a certain angle about a point called the center of rotation
*Unless stated otherwise, rotations are counterclockwise
Rotation Rules (around the origin):
90° (x, y)  (-y, x)
180° (x, y)  (-x, -y)
270° (x, y)  (y, -x)
Ex7) Find the image of P(-2,-2) after being rotated 180° about the origin.

8. Rotations
Ex8) Find the image of Z(1,-4) after being rotated 270° about the origin.
Ex9) Given the points X(0,-1), Y(1,2), Z(4,1), draw ΔXYZ and its rotation of 90° about the origin.

9. Transformations
Ex 10) Use P(-5,3) as the preimage for each of the following transformations:
Q) Translation: P
R) Reflection over:
S) Rotation of 270° about the origin

10. Transformations
Ex11) Find the image of point X(-1, 5) after being translated 4 to the right, reflected across y-axis, and then rotated 180° about the origin.

11. Transformations
Ex12) What type of transformation is represented by each figure? a) b) c)

12. p.487 #31, 34 (about the origin ONLY)
ON GRAPH PAPER!!!
Homework #26:
p.473 #9-14, 22
p.480 #1-13 odd
p.487 #31, 34 (about the origin ONLY)