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1.2: Transformations

CCSS.

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1.2: Transformations

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  1. CCSS G-CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G-CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G-CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G-CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. 1.2: Transformations G-CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

  2. Rotation (turn) • Need the center of rotation labeled • Need the angle of rotation labeled A’ A 90o angle of rotation, clockwise. Center of rotation **Unless specified, all rotations are done COUNTERCLOCKWISE

  3. The Rule • The general rule for a rotation counterclockwise about the origin by 90° is (X,Y) => (-Y, X) http://www.mathwarehouse.com/transformations/rotations-in-math.php

  4. Rotate ABC 270 degrees counterclockwise

  5. 1.RST has vertices at R(0, 3), S(4, 0), and T(0, 0). Find the coordinates of R after a 180º clockwise rotation about T. 2.FGH has vertices F(−1, 2), G(0, 0), and H(3, −1). Find the coordinates of F after a 270° clockwise rotation about G.

  6. Translation (slide) • Slide all parts of the figure the same distance and direction (slide it) A A’

  7. Translation in coordinate plane If ΔABC with A(-1,-3), B(1,-1), & C(-1,0), Find the coordinates of the image after the translation: (x,y) (x-3,y+4) Subtract 3 from all x’s Add 4 to all the y’s

  8. ΔABC A (-1,-3) B (1,-1) C (-1,0) ΔA’B’C’ A’ (-4,1) B’ (-2,3) C’ (-4,4) Finding the new points (x,y) => (x-3,y+4)

  9. Find the coordinates of Under the translation of (x-1, y-3)

  10. Write the translation for this picture (x,y) ( x , y ) (2,4) (-5,1) (2,1) (-5,-2)

  11. Notation for transformations Write in what the notation means

  12. The end

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