1 / 17

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.

zoerobb
Download Presentation

Constructions of Basic Transformations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related