Chapter 14 (Sp10)

# Chapter 14 (Sp10) - Section 14-1 Translations and Rotations...

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Section 14-1 – Translations and Rotations Translation (slide): When an object moves a certain distance in a certain direction along a line preserving the length and angles in the figure. A motion of a place that moves every point of the plane a specified distance in a specified direction along a straight line. A A′ Any rigid motion that preserves length or distance is called an isometry . Example : Find the image of the figure under the translation from X to X′ on the dot paper. x x′ x x′ 1

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-5 -4 -3 -2 -1 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 Coordinate Representations of Translations Point Image Point ( x , y ) A translation is a function from the plane to the plane such that every point ( x , y ) corresponds to the point ( ________, ________) where a and b are real numbers. Symbolically, we write: Example : Draw the image of the figure under the translation: ( 29 ( 29 x,y x 3,y 4 - + . 2
-5 -4 -3 -2 -1 1 2 3 4 5 -6 -5 -4 -3 -2 -1 1 2 3 4 5 Another type of isometry is a Rotation (turn) . Rotation: A transformation of the plane determined by holding one point (the center) fixed and rotation the plane about this point by a certain amount in a certain direction. To determine a rotation, we need three pieces of information: 1. The turn center 2. The direction of the turn (clockwise or counterclockwise) 3. The amount of the turn A B C O Example : Find the image of triangle ABC in a counterclockwise 90° rotation about point O. O

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Chapter 14 (Sp10) - Section 14-1 Translations and Rotations...

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