1. Transformations and Tessellations Edited By: K. Stone

2. Transformation Movements of a figure in a plane May be a SLIDE, FLIP, or TURN

3. Translation Another name for a SLIDE A B C A’ C’ B’ A’, B’ and C’ are explained in the next slide...

4. Image The figure you get after a translation Original Image Slide AA’ BB’CC’ The symbol ‘ is read “prime”. ABC has been moved to A’B’C’. A’B’C’ is the image of ABC.

5. Writing a Rule Finding the amount of movement LEFT and RIGHT and UP and DOWN

6. Writing a Rule 9 8 7 6 5 4 3 2 1 0123456789 Right 4 (positive change in x) Down 3 (negative change in y) A A’ B B’ C C’

7. Writing a Rule Can be written as: R4, D3 (Right 4, Down 3) (x+4, y-3)

8. Reflection Another name for a FLIP AA’ CC’BB’

9. Reflection Used to create SYMMETRY on the coordinate plane

10. Symmetry When one side of a figure is a MIRROR IMAGE of the other

11. Line of Reflection The line you reflect a figure across Ex: X or Y axis

12. Rotation Another name for a TURN B B’ C C’ A A’

13. Rotation A transformation that turns about a fixed point

14. Center of Rotation The fixed point (0,0) A A’ C C’ B B’

15. Rotational Symmetry When an image after rotation of 180 degrees or less fits exactly on the original

16. Rotating a Figure Measuring the degrees of rotation 90 degrees A A’ C C’ B B’

17. Tessellation A design that covers a plane with NO GAPS and NO OVERLAPS

18. Tessellation Formed by a combination of TRANSLATIONS, REFLECTIONS, and ROTATIONS

19. Pure Tessellation A tessellation that uses only ONE shape

20. Pure Tessellation

22. Semiregular Tessellation A design that covers a plane using more than one shape

23. Semiregular Tessellation

27. What will tessellate? In order to tessellate, shapes must fit together to form 360 ○ at their vertex. To find out if a shape will tessellate a plane alone, divide the measure of one of its angles into 360. If it divides evenly, it will tessellate. If not, it won’t. For example, a square has 90 ○ angles. 90 goes into 360 exactly 4 times, so a square will tessellate by itself.

28. Tessellation Used famously in artwork by M.C. Escher

31. LINKS Cool math Lessons - Geometry - What are Tessellations?Cool math Lessons - Geometry - What are Tessellations? Interactivate: Tessellate!