Translations, Reflections, & Rotations

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Presentation transcript:

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

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

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.

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

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.

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.

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.

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.

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

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.

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

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)