Slide to the Left, Slide to the Right!!!

1. Slide to the Left, Slide to the Right!!! Transformations 
on the 
Coordinate Plane Rotations Dilations Dilations Rotaions Reflections Translations Translations

2. What type of transformation does each of these graphs represent? How can you tell? 3 1 2

3. What type of transformation does this graph represent? How can you tell? B A B’ C’ D C A’ D’

4. Review of Transformations • Dilation • Dilation makes an image larger or smaller. • It moves a figure on a fixed center using a scale factor. • A scale factor greater than 1 enlarges; less than 1 shrinks. • Translation • Translation slides a figure up or down, and left or right. • The figure’s size and shape are unchanged. • Reflection • Reflection “flips” a figure across the x-axis or y-axis. • The figure’s size and shape are unchanged. • We use “prime” notation • when identifying new coordinates. • Rotation • Rotation moves a figure around a fixed center.

5. Summary of Transformation Formulas How the coordinates of each point change with each type of transformation. Reflection across the x- axis Reflection across the y- axis Translation Dilation Rotation 90º counterclockwise Rotations 90˚ clockwise Rotation 180º (x, y) goes to (x, -y) (x, y) goes to (-x, y) (x, y) goes to (x + a, y + b) (x, y) goes to (kx, ky) (x, y) goes to (-y, x) (x, y) goes to (y, -x) (x, y) goes to (-x, -y)

6. Dilation Dilation makes an image larger or smaller. The size of the figure changes. The shape of the figure stays the same. It moves a figure on a fixed center using a scale factor. A scale factor greater than 1 enlarges; less than 1 shrinks. A B Original figure: A: (-4, 8) B: (6, 8) C: (6, -6) D: (-4,-6) D C Figure after dilation: A’: (-2, 4) B’: (3, 4) C’: (3, -3) D’: (-2, -3) What are the points? What is the dilation factor? Dilation factor k= ½

7. Translation The figure stays the exact same size and shape. Each point moves the same amount: to the left or right, and up or down. Original Figure: A: (2,1) B: (6,1) C: (4,4) C A B C’ Translated figure: A’: (4,-4) B’: (8,-4) C’: (6,-1) A’ B’ What are the points? Describe the steps in this translation. Translation: 2 units right and 5 units down

8. Reflection across the y-axis D D’ Original figure: A: (4, 2) B: (8, 2) C: (9 ,6) D: (6, 9) E: (3, 6) E’ C’ E C A’ B’ A B Reflected figure: A’: (-4, 2) B’: (-8, 2) C’: (-9, 6) D’: (-6, 9) E’: ( -3, 6) What are the points? How have the coordinates for the points of the original figure been changed when the figure is reflected across the y-axis ? What would be the coordinates if the original figure were reflected across the x-axis ?

9. 180˚ Rotation Around The Origin Original Figure: A: (4, 2) B: (6, 2) C: (3.5, 4) D: (6.5, 4) E: (5, 5) Figure after rotation: A’: (-4, -2) B’: (-6, -2) C’: (-3.5, -4) D’: (-6.5, -4) E’: (-5, -5) Draw a sketch. What are these points? How have the coordinates of the original figure been changed by the 180˚ rotation around the origin?

10. Practice with transformations C A B R P Q Show that D ABC is congruent to D PQR with a reflection followed by a translation. If you reverse the order of the reflection and translation in part (a), does D ABC still map to D PQR ? Find another way, different from part (a) or (b), to map D ABC to D PQR, using translations, rotations, and/or reflections.

11. Transformations Project • For this project, you will create a poster • to demonstrate your knowledge of transformations. • For each type of transformation, you will do the following on a separate graph: • Start by graphing a figure and its transformation on a sheet of graph paper. • Use 2 different colors to distinguish the the original figure from its transformation. • Label each graph with a title telling what type of transformation it shows. • Each graph should be a different original image. • Label each vertex of the original image, then use the “prime” notation to label the corresponding vertices of the new image. • Write a paragraph explaining the transformation ReflectionRotationTranslationDilation The Paragraph Write a paragraph about your transformations. Describe each transformation in your own words. Include important information about each transformation such as line of reflection, point of rotation, degrees and direction of rotation, and specifics about the translation. Write or print neatly and use proper grammar and spelling. Organize your transformation graphs and summary paragraph on a poster board. (Minimum size: half of a full size poster board). Make this neat and colorful. You will have one class period to work during school; you may need to complete the project outside of class time. Use the rubric below to be sure you have included everything. Score yourself on your project and record your scores in the rubric. Good luck and have fun!