1. Warm-up
Begin at the word “A.” Every time you move, write down the word(s) upon which you land.
heart
dream a
1. Move to the consecutive interior angle.
2. Move to the alternate interior angle.
makes
3. Move to the corresponding. A
4. Move to the alternate exterior.
5. Move to the exterior linear pair.
wish is
6. Move to the alternate exterior angle.
your
7. Move to the vertical angle.

2. RIGID TRANSFORMATIONS The preimage and image are congruent.
Geometry in Motion
RIGID TRANSFORMATIONS
The preimage and image are congruent.
* Translations
* Reflections
* Rotations

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. Translating slides the object up, down, left, right.

8. Translation (slide)
(x,y)(x – 2, y + 2) B C A
Move left 2
then up 2

9. (x,y)(x +5, y ) E
Move right 5 G F

10. Reflect over the x-axis Reflect over the y-axis
Reflections
Reflect over the x-axis
Reflect over the y-axis

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

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

13. Example: Reflect over the x-axis
3 -1
-3 3
1 4

14. Reflect over the x-axis

15. Reflect over the x-axis

16. Reflect over the x-axis

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

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

19. Example: Reflect over the y-axis
-2 4
1 8
4 -4

20. Reflect over the y-axis

21. Reflect over the y-axis

22. Reflect over the y-axis

23. Reflect over the y-axis
Odd Shapes
Reflect over the y-axis

24. Rotations

25. Rotation is simply turning about a fixed point.
For our purposes, the fixed point will be the origin
Rotate
90 counterclockwise
about the origin
Rotate
180
about the origin
Rotate 90clockwise about the origin

26. CLOCKWISE
is a right turn.

27. Hands in the air on the wheel.
Left hand is x
Right hand is y

28. Which hand is at 12 o’clock first?
Make a clockwise turn.
Which hand is at 12 o’clock first? X

29. Rotate 90 degrees clockwise.
Change the sign of x
&
switch the order of x and y.

30. Example: Rotate 90 degrees clockwise.

31. Rotate 90° clockwise
3 7
4 -1
1 -3

32. Rotate 90° clockwise

33. COUNTERCLOCKWISE
is a left turn.

34. Hands in the air on the wheel.
Left hand is x
Right hand is y

35. Make a counterclockwise turn.
Which hand is at 12 o’clock first? Y

36. Rotate 90 degrees counterclockwise.
Change the sign of y
&
Switch the order of x and y

37. Example: Rotate 90 degrees counterclockwise.

38. Rotate 90° counterclockwise

39. Rotate 90° counterclockwise

40. Rotating 180 degrees changes the sign of the x and the sign of the y.

41. change the sign of both x & y.
Rotate 180 degrees.
Keep the order
&
change the sign of both x & y.

42. Example: Rotate 180 degrees.

43. Rotate 180°

44. Rotate 180°

45. The image and preimage are similar.
Dilations
REDUCTIONS
ENLARGEMENTS
Your image is smaller than your original
Your image is larger than your original
Scale Factor is a fraction between zero and one
Scale Factor is a number bigger than one
The image and preimage are similar.
Dilations are not a rigid transformation.

46. All you do is multiply k to (x, y).
Find the coordinates of the dilation image for the given scale factor, k.
Example 1:
G(0, -2), H(1, 3), and I(4, 1); k = 2
All you do is multiply k to (x, y).
G’( , ), H’( , ), and I’( , )

47. All you do is multiply k to (x, y).
Find the coordinates of the dilation image for the given scale factor, k.
Example 2:
L(8, -8), N(0, 16), and M(4, 5); k = 1/4
All you do is multiply k to (x, y).
L’( , ), N’( , ), and M’( , )

48. k = 1/2

49. k = 2

50. Practice Does the Brain Good.
Translations, Reflections,
Rotations & Dilations Practice
Practice
Finish

51. Warm-up
Begin at the word “A”. Every time you move, write down the word(s) upon which you land.
heart
dream a
1. Move to the consecutive interior angle.
2. Move to the alternate interior angle.
makes
3. Move to the corresponding. A
4. Move to the alternate exterior.
5. Move to the exterior linear pair.
wish is
6. Move to the alternate exterior angle.
your
7. Move to the vertical angle.

52. ______ TRANSFORMATIONS The preimage and image are _________.
Geometry in Motion
______ TRANSFORMATIONS
The preimage and image are _________.
* Translations
* Reflections
* Rotations

53. * Translations
(____ your image over)
* image
* preimage

54. * Reflections
(____ your image over)
* preimage
* image

55. (____ your image about a fixed point)
* Rotations
(____ your image about a fixed point)
* image
* preimage

56. What are the different transformations?

57. Translating slides the object up, down, left, right.

58. Translation (slide)
(x,y)(x – 2, y + 2) B C A

59. (x,y)(x +5, y ) E G F

60. Reflect over the x-axis Reflect over the y-axis
Reflections
Reflect over the x-axis
Reflect over the y-axis

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

62. Example: Reflect over the x-axis

63. Reflect over the x-axis

64. Reflect over the x-axis

65. Reflect over the x-axis

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

67. Example: Reflect over the y-axis

68. Reflect over the y-axis

69. Reflect over the y-axis

70. Reflect over the y-axis

71. Reflect over the y-axis
Odd Shapes
Reflect over the y-axis

72. Rotations

73. Rotation is simply turning about a fixed point (the origin).
Rotate
90 counterclockwise
about the origin
Rotation is simply turning about a fixed point (the origin).
Rotate 90clockwise about the origin
Rotate
180
about the origin

74. CLOCKWISE
is a ______ turn.

75. Rotate 90 degrees clockwise.
Change the sign of x
&
switch the order of x and y.

76. Example: Rotate 90 degrees clockwise.

77. Rotate 90° clockwise

78. Rotate 90° clockwise

79. COUNTERCLOCKWISE
is a ______ turn.

80. Rotate 90 degrees counterclockwise.
Change the sign of y
&
Switch the order of x and y

81. Example: Rotate 90 degrees counterclockwise.

82. Rotate 90° counterclockwise

83. Rotate 90° counterclockwise

84. change the sign of both x & y.
Rotate 180 degrees.
Keep the order
&
change the sign of both x & y.

85. Example: Rotate 180 degrees.

86. Rotate 180°

87. Rotate 180°

88. The image and preimage are ______.
Dilations
REDUCTIONS
ENLARGEMENTS
Your image is smaller than your original
Your image is larger than your original
Scale Factor is a fraction between zero and one
Scale Factor is a number bigger than one
The image and preimage are ______.
Dilations are ____ a ______ transformation.

89. All you do is multiply k to (x, y).
Find the coordinates of the dilation image for the given scale factor, k.
Example 1:
G(0, -2), H(1, 3), and I(4, 1); k = 2
All you do is multiply k to (x, y).
G’( , ), H’( , ), and I’( , )

90. All you do is multiply k to (x, y).
Find the coordinates of the dilation image for the given scale factor, k.
Example 2:
L(8, -8), N(0, 16), and M(4, 5); k = 1/4
All you do is multiply k to (x, y).
L’( , ), N’( , ), and M’( , )

91. k = 1/2

92. k = 2

93. Practice Does the Brain Good.
Translations, Reflections,
Rotations & Dilations Practice
Practice
Finish