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. A change in size occurs in dilations.

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

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:

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:

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:

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

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?

Working With Translations 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 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’?

Working With Reflections 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 How do you think the coordinates would change if you reflected CAKE over the y-axis?

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’’?

Working With Reflections 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 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’. How did the coordinates change mathematically in T’O’Y’?

Working With Rotations 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 Object TOY T(5,3) O(2,8) Y(8,8) (x,y) Do you think the same changes in the coordinates would occur if you rotated the polygon counter-clockwise? Try it to find out.

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’’?

Working With Rotations 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