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Constructions of Basic Transformations

Constructions of Basic Transformations. Transformations. The mapping, or movement, of all the points of a figure in a plane according to a common operation. A change in size or position occurs with transformations. A change in position occurs in translations, reflections and rotations.

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Constructions of Basic Transformations

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  1. Constructions of Basic Transformations

  2. Transformations • The mapping, or movement, of all the points of a figure in a plane according to a common operation. • A change in size or position occurs with transformations. • A change in position occurs in translations, reflections and rotations. • A change in size occurs in dilations.

  3. Translation Rotation Reflection Dilation Image Object (Pre-Image) Congruent Similar Scale Factor Symmetry Reflectional symmetry Rotational symmetry Enlargement Reduction Center of Rotation Congruent Vocabulary

  4. Translation (slide) • A transformation that “slides” each point of a figure the same distance in the same direction. • A translation will be a congruent figure. • Example:

  5. Reflection (flip) • A transformation that “flips” a figure over a line of reflection. • A mirror image is created. • A reflection will be a congruent figure. • Example:

  6. Rotation (turn) • A transformation that turns a figure about a fixed point through a given angle and a given direction. • A rotation will be a congruent figure. • Example:

  7. Quadrant I y-axis Quadrant II x-axis Quadrant III Quadrant IV

  8. Working With Translations • Plot polygon RAKE on a coordinate plane using vertices R(3,3), A(3,6), K(8,6), and E(8,3). • Label the coordinates and connect the vertices. • Color in the polygon. • Translate RAKE 5 units down and 1 unit right (1,-5). Label the image R’A’K’E’ (Prime). • Compare the size, location, and coordinates of the pre-image (original) and the image. • What happened mathematically to the coordinates (x,y) of the vertices after RAKE was translated?

  9. Object RAKE R(3,3) A(3,6) K(8,6) E(8,3) (x,y) Image R’A’K’E’ R’(4,-2) A’(4,1) K’(9,1) E’(9,-2) (x+1,y-5) Working With Translations

  10. Working With Reflections • Plot polygon CAKE on a coordinate plane using vertices C(3,3), A(3,6), K(8,6), and E(8,3). • Label coordinates and connect the vertices. • Color in the polygon. • Reflect CAKE over the x-axis. • Label coordinates of C’A’K’E’ and color in the polygon. • How did the coordinates change on the image C’A’K’E’?

  11. Object CAKE C(3,3) A(3,6) K(8,6) E(8,3) (x,y) Image C’A’K’E’ C’(3,-3) A’(3,-6) K’(8,-6) E’(8,-3) (x,-y) when reflected over the x-axis Working With Reflections How do you think the coordinates would change if you reflected CAKE over the y-axis?

  12. Working With Reflections • On the same coordinate plane, reflect CAKE over the y-axis. • Label coordinates of the image C’’A’’K’’E’’ and color in the polygon. • How did the coordinates change on the image C’’A’’K’’E’’?

  13. Object CAKE C(3,3) A(3,6) K(8,6) E(8,3) (x, y) Image C’’A’’K’’E’’ C’’(-3,3) A’’(-3,6) K’’(-8,6) E’’(-8,3) (-x, y) when reflected over the y-axis Working With Reflections

  14. Working With Rotations • Plot polygon TOY on a coordinate plane using vertices T(5,3), O(2,8) and Y(8,8). • Label the coordinates and connect the vertices. • Color in the polygon. • Rotate TOY 90 degrees clockwise about the Origin. (Use a protractor and a ruler. Make sure each vertex and it’s prime are the same distance away from the Origin.) • Label the coordinates of the image T’O’Y’. • Color in the polygon. • How did the coordinates change mathematically in T’O’Y’?

  15. Object TOY T(5,3) O(2,8) Y(8,8) (x,y) Image T’O’Y’ rotated 90 degrees clockwise T’(3,-5) O’(8,-2) Y’(8,-8) (y,-x) when the image is rotated 90 degrees clockwise Working With Rotations Do you think the same changes in the coordinates would occur if you rotated the polygon counter-clockwise? Try it to find out.

  16. Working With Rotations • On the same coordinate plane, rotate TOY 180 degrees clockwise about the Origin. (Use a protractor and a ruler. Make sure each vertex and it’s prime are the same distance away from the Origin.) • Label the coordinates of the image T’’O’’Y’’. • Color in the polygon. • How did the coordinates change mathematically in T’’O’’Y’’?

  17. Object TOY T(5,3) O(2,8) Y(8,8) (x,y) Image T’’O’’Y’’ rotated 180 degrees clockwise T’’(-5,-3) O’’(-2,-8) Y’’(-8,-8) (-x,-y) when rotated 180 degrees Working With Rotations

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