1. Rigid Motion in a Plane
* Translations
* Reflections
* Rotations

2. MC Esher

3. * Translations
(Slide your image over)
* image
* preimage

4. * Reflections
(Flip your image over)
* preimage
* image

5. (Turn your image about a fixed point )
* Rotations
(Turn your image about a fixed point )
* image
* preimage

6. What are the different transformations?

7. Naming Transformations
Name and describe the transformation.
Name two angles with the same measure.
Reflection in the line x = -2
B and F
D and H
etc.

8. In the figure, XYZ → ABC by a transformation
In the figure, XYZ → ABC by a transformation. Name the transformation and the image of X. X
Reflection about the line. Z Y B C A

9. Every segment is congruent to its image.
Transformations are called RIGID if every image is congruent to its preimage.
Rigid transformations can also be referred to as an ISOMETRY.
Every segment is congruent to its image.

10. Which of the following are rigid transformations? (Isometry)

11. they preserve angle measures
Isometries not only
preserve lengths, but
they preserve angle measures
parallel lines, and
betweenness of points

12. Find the value of each variable, given that the transformation is an isometry.

13. Translations

14. B C A Translate by (-2, 2). Find the new coordinates and graph.
Move left 2
then up 2

15. E G F Translate by (5, 0). Find the new coordinates and graph.
Move right 5 G F

16. Find the coordinates if each point is translated by (-2, 5)
A(1, 2) B(4, 1) C(-1, -2)
A'(-1, 7) B'(2, 6) C'(-3, 3)

17. Sketch the image of the triangle after the translation (x, y)(x + 5, y – 3)
(-2,4)
(-6,1)
(3,1)
(-4,0)
(-1,-2)
(1,-3)

18. Reflections

19. Reflecting across the x-axis… changes the sign of the .

20. Reflect over the x-axis
Change the sign of the y

21. Example: Reflect over the x-axis

22. Reflect over the x-axis

23. Reflecting across the y-axis… changes the sign of the .

24. Reflect over the y-axis
Change the sign of the x

25. Example: Reflect over the y-axis

26. Reflect over the y-axis

27. Reflections in a Coordinate Plane
Graph the given reflections.
A(3, 2) in the y-axis
B(1, -3) in the line y = 1
A’(-3, 2)
B’(1, 5)

28. Line of symmetry – a line that can be drawn through a figure so that the part of the figure on one side of the line is the congruent reflected image of the part on the other side of the line.

30. Animals that have Line Symmetry
Here are a few more great examples of mirror image in the animal kingdom.
                                                 
                                           
                                          
                                  

32. The Taj Mahal
Symmetry exists in architecture all around the world.  One of the best known examples of this is the Taj Mahal.  
                                                                                                                    
It was completed in 1630 by the Indian ruler Shahs Jahan as a tomb for his favorite wife Mumtaz Mahal who died as a result of giving birth to their 14th child. To build this tomb it took 20,000 workers, 20 years (Encarta 97) and it is rumoured that they used 40,000 elephants to transport the materials.  

33.                                            
Symmetry of Drains
   
                                           
Drains can have many different orders of rotational symmetry,
Have a look at some of the drains in your home or at school and see what order of rotation or line symmetry they have.

34. These masks have a line of symmetry from the forehead to the chin.
                                                                                                                                                 

35. Ex. Determine the number of lines of symmetry in the quadrilateral

36. Ex. 1: Find all lines of symmetry.

37. Symmetry is found everywhere in nature and is also one of the most prevalent themes in art, architecture, and design.
Symmetry is certainly one of the most powerful and pervasive concepts in mathematics.

38. Japanese culture dislike exact symmetry more than conventional Western culture.
Symmetry appears as being too perfect for their liking. It is too unnatural and sterile.
The Japanese hold the view that their lives always need refinement and room for growth, complete symmetry implies perfection and so is undesirable.

39. If something has a pattern it is easier to spot the out of place and therefore possibly dangerous.

40. Most plants and animals are symmetrical
Symmetrical flowers are more attractive to bees because they have more nectar.

41. Symmetric objects are usually more pleasing to look at than asymmetric ones.

42. Symmetry is an indication of both youthfulness and health.

43. Denzel Washington is said to have a very symmetrical face.

44. Greta Garbo was known for having a very symmetrical face.

45. “Christy Turlington has attributed much of her success as an advertising icon to the perfect symmetry of her lips.”

46. Facial asymmetry is an indication of aging.

47. Right Left The Original Photo
Is the Face Really Symmetrical?
Right Left The Original Photo

48. Right Left The Original Photo
Is the Face Really Symmetrical?
Right Left The Original Photo

49. Right Left The Original Photo
Right / right
Left / left
The Original Photo
Is the Face Really Symmetrical?
Right Left The Original Photo

50. Assignment
Goes
Here