1. Penair School Menu x y x x - x Transformations

2. Penair School Menu Transformations 1. Examples of different Transformation 2. Transformation “Jungles” 3. Predicting Activity (Three levels) Individual transformations explained plus sets of four descriptions to draw. Questions on diagrams containing a large number of shapes. List the shapes that fit. Questions on diagrams containing a large number of shapes. List the shapes that fit. Menu

3. Penair School Menu Transformations Menu Written descriptions only Descriptions and Diagrams A Translations B Reflections C Rotations D Enlargements 12345678 12345678 12345678 12345678 A Translations B Reflections C Rotations D Enlargements 1 - 45 - 8 1 - 45 - 8 1 - 45 - 8 1 - 45 - 8 Jungle 1 Question Menu Jungle 2. Question Menu Basic translations, reflections + rotations. 123456 123456 123456 Basics + new lines of reflection... More enlargements, centres, SF’s etc.

4. Penair School Menu Pressing keys or clicking moves slides on. Pressing P goes to previous slide. SLIDE CONTROL WHEN IN PRESENTATION MODE Using menu slide, click on chosen button to go to that slide. Click on Menu button to return. In presentation mode, right click, then ‘help’ gives a full list of control options.

5. Penair School Menu What is this? What type of movement does this picture make you think of? Rotation

6. Penair School Menu What is this? What type of mapping does this picture make you think of? Reflection

7. Penair School Menu What about this? What type of mapping does this picture make you think of? Enlargement??

8. Penair School Menu What is this? What type of mapping does this picture make you think of? Translation

9. Penair School Menu Examples of Transformations Written descriptions only Descriptions and Diagrams This section looks at various types of basic transformation. The written descriptions are given so that drawings can be attempted before viewing. The other part describes and demonstrates each transformation one at a time.

10. Penair School Menu Examples of Translations Use triangle with coordinates (-4, 0 ), ( -2, 0) and ( -4, 3 ) 5 2 Translation of 5 to the right and 2 up 1 7 1 Translation of 7 to the right and 1 up 2 34 2 2 Translation of 2 to the right and 2 up 5 - 3 Translation of 5 to the right and 3 down

11. Penair School Menu Examples of Translations Use triangle with coordinates ( 2, 0 ), ( 4, 0) and ( 2, 3 ) 56 78 0 - 5 Translation of 0 across and 5 down - 4 2 Translation of 4 to the left and 2 up - 6 - 4 Translation of 6 to the left and 4 down - 5 1 Translation of 5 to the left and 1 up

12. Penair School Menu Examples of Reflections Use triangle with coordinates (1, 2 ), ( 3, 2) and ( 1, 5 ) 12 34 Reflection in the line x = - 1 Reflection in the x axis Reflection in the y axis Reflection in the line y = 1

13. Penair School Menu Examples of Reflections Use triangle with coordinates ( 3, 0 ), ( 5, 0) and ( 5, 3 ) 56 78 Reflection in the line y = x Reflection in the line y = - x Reflection in the line y = x - 1 Reflection in the line x = 1.5

14. Penair School Menu Examples of Rotations Use L- shape with coordinates ( 1, 0 ), ( 4, 0), ( 4, 2 ), ( 3, 2 ), ( 3, 1 ) and ( 1, 1 ) 12 34 Rotation of + 90 o about ( 0, 0 ) Rotation of + 180 o about ( 0, 0 ) Rotation of - 90 o about ( 0, 0 ) Rotation of + 90 o about ( 1, - 2 )

15. Penair School Menu Examples of Rotations Use L- shape with coordinates ( 1, 0 ), ( 4, 0), ( 4, 2 ), ( 3, 2 ), ( 3, 1 ) and ( 1, 1 ) 56 78 Rotation of + 180 o about ( 0, 2 ) Rotation of - 90 o about ( 1, 0 ) Rotation of 180 o about ( 0, 1 ) Rotation of + 90 o about ( 2.5, 0 )

16. Penair School Menu Examples of Enlargements 12 34 (-1,-1), (5,-1), (-1,-5) Enlargement of scale factor + 0.5 centre ( - 1, 5 ) (0,-3), (3,-3), (3,-1) Enlargement of scale factor + 3 centre ( 2, - 4 ) (-3,2), (0,2), (0,4) Enlargement of scale factor + 2 centre ( - 5, 3 ) (-1,3), (1,4), (-1,4) Enlargement of scale factor + 5 centre ( 0, 5 )

17. Penair School Menu Examples of Enlargements 56 78 (-1,-1), (5,-1), (-1,-5) Enlargement of scale factor + 0.5 centre ( - 1, 5 ) (-1,3), (1,4), (-1,4) Enlargement of scale factor + 5 centre ( 0, 5 ) (-2,-1), (2,3), (-2,3) Enlargement of scale factor + 0.5 centre ( 4, - 3 ) (-2,-1), (2,3), (-2,3) Enlargement of scale factor + 0.5 centre ( 4, - 3 )

18. Penair School Menu A1 x y Blue = Object Red = Image 5 2 Translation of 5 to the right and 2 up

19. Penair School Menu A2 x y Blue = Object Red = Image 7 1 Translation of 7 to the right and 1 up

20. Penair School Menu A3 x y Blue = Object Red = Image 2 2 Translation of 2 to the right and 2 up

21. Penair School Menu A4 x y Blue = Object Red = Image 5 - 3 Translation of 5 to the right and 3 down

22. Penair School Menu A5 x y Blue = Object Red = Image 0 - 5 Translation of 0 across and 5 down

23. Penair School Menu A6 x y Blue = Object Red = Image - 4 2 Translation of 4 to the left and 2 up

24. Penair School Menu A7 x y Blue = Object Red = Image - 5 1 Translation of 5 to the left and 1 up

25. Penair School Menu A8 x y Blue = Object Red = Image - 6 - 4 Translation of 6 to the left and 2 down

26. Penair School Menu B1 x y Blue = Object Red = Image Reflection in the x axis

27. Penair School Menu B2 x y Blue = Object Red = Image Reflection in the y axis

28. Penair School Menu B3 x y Blue = Object Red = Image Reflection in the line y = 1

29. Penair School Menu B4 x y Blue = Object Red = Image Reflection in the line x = - 1

30. Penair School Menu B5 x y Blue = Object Red = Image Reflection in the line y = x

31. Penair School Menu B6 x y Blue = Object Red = Image Reflection in the line x = 1.5

32. Penair School Menu B7 x y Blue = Object Red = Image Reflection in the line y = x - 1

33. Penair School Menu B8 x y Blue = Object Red = Image Reflection in the line y = - x

34. Penair School Menu C1 x Blue = Object Red = Image Rotation of + 90 o about ( 0, 0 ) y +

35. Penair School Menu C2 x y Blue = Object Red = Image Rotation of + 180 o about ( 0, 0 ) +

36. Penair School Menu C3 x y Blue = Object Red = Image Rotation of - 90 o about ( 0, 0 ) +

37. Penair School Menu C4 x y Blue = Object Red = Image Rotation of + 90 o about ( 1, - 2 ) + x

38. Penair School Menu C5 x y Blue = Object Red = Image Rotation of 180 o about ( 2.5, 0 ) + x

39. Penair School Menu C6 x y Blue = Object Red = Image Rotation of 180 o about ( 0, 1 ) + x

40. Penair School Menu C7 x y Blue = Object Red = Image Rotation of - 90 o about ( 1, 0 ) + x

41. Penair School Menu C8 x y Blue = Object Red = Image Rotation of + 180 o about ( 0, 2 ) + x

42. Penair School Menu D1 x y Blue = Object Red = Image (-1,0), (3,2), (-1,2) Enlargement of scale factor + 2 centre ( 1, 4 ) x

43. Penair School Menu D2 x y Blue = Object Red = Image (0,-3), (3,-3), (3,-1) Enlargement of scale factor + 3 centre ( 2, - 4 ) x

44. Penair School Menu D3 x y Blue = Object Red = Image (-3,2), (0,2), (0,4) Enlargement of scale factor + 2 centre ( - 5, 3 ) x

45. Penair School Menu D4 x y Blue = Object Red = Image (-1,3), (1,4), (-1,4) Enlargement of scale factor + 5 centre ( 0, 5 ) x

46. Penair School Menu (-3,0), (0,0), (0,2) Enlargement of scale factor + 2 centre ( - 5, 3 ) D5 x y Blue = Object Red = Image x

47. Penair School Menu (-2,-1), (2,3), (-2,3) Enlargement of scale factor + 0.5 centre ( 4, - 3 ) D6 x y Blue = Object Red = Image x

48. Penair School Menu D7 x y Blue = Object Red = Image (-1,1), (-1,-1), (3,1) Enlargement of scale factor + 1.5 centre ( 1, 5 ) x y x

49. Penair School Menu D8 x y Blue = Object Red = Image (-1,-1), (5,-1), (-1,-5) Enlargement of scale factor + 0.5 centre ( - 1, 5 ) y x

50. Penair School Menu Return to Main Menu Transformation “Jungles” Jungle 1. Question Menu Jungle 2. Question Menu Click Here for Rules of Jungle Each diagram shows a “Jungle” of shapes. The challenge is to name the shapes that fit the description. There are often several answers.

51. Penair School Menu 1 1.Reflection in the y axis 2.Translations 3.Rotations of 180 o about (0,0) 4.Reflection in the x axis 5.Rotation of 90 o about (0,0) 6.Rotation of 180 o about (7,0) 7.Reflections in the x = c lines 8.Possible “glide reflections” Transformation Jungle 1

52. Penair School Menu x y B A E F I G K D H C J L 1.Reflection in the y axis 1 Return to Questions

53. Penair School Menu x y B A E F I G K D H C J L 1.Reflection in the y axis 1 Return to Questions

54. Penair School Menu x y B A E F I G K D H C J L 2. Translations 1 Return to Questions

55. Penair School Menu x y B A E F I G K D H C J L 2.Translations 1 Return to Questions

56. Penair School Menu x y B A E F I G K D H C J L 1 3. Rotations of 180 o about (0,0) Return to Questions

57. Penair School Menu x y B A E F I G K D H C J L 3. Rotations of 180 o about (0,0) 1 Return to Questions

58. Penair School Menu x y B A E F I G K D H C J L 4.Reflection in the x axis 1 Return to Questions

59. Penair School Menu x y B A E F I G K D H C J L 4.Reflection in the x axis 1 Return to Questions

60. Penair School Menu 5. Rotations of 90 o about (0,0) x y B A E F I G K D H C J L 1 Return to Questions

61. Penair School Menu x y B A E F I G K D H C J L 5. Rotations of 90 o about (0,0) 1 Return to Questions

62. Penair School Menu x y B A E F I G K D H C J L 6. Rotation of 180 o about (7,0) 1 Return to Questions

63. Penair School Menu x y B A E F I G K D H C J L 6. Rotation of 180 o about (7,0) 1 Return to Questions

64. Penair School Menu x y B A E F I G K D H C J L 1 7. Reflection in the x = c lines Return to Questions

65. Penair School Menu x y B A E F I G K D H C J L 7. Reflection in the x = c lines 1 Return to Questions

66. Penair School Menu x y B A E F I G K D H C J L 1 8. Possible “glide reflections” Return to Questions

67. Penair School Menu x y B A E F I G K D H C J L 1 8. Possible “glide reflections” Return to Questions

68. Penair School Menu 2 1. Rotation of 180 o about (0,0) 2. Reflections in the y = c lines 3.Rotations of 90 o about (0,0) 4.Translations 5. Reflections in the x = c lines 6.Rotations of 180 o 7. Rotations of 90 o 8.Possible “glide reflections” Transformation Jungle 2

69. Penair School Menu x y A L F I G K B J E 2 1. Rotation of 180 o about (0,0) D C H M Return to Questions

70. Penair School Menu x y A L F I G K B J E 2 1. Rotation of 180 o about (0,0) D C H M Return to Questions

71. Penair School Menu x y A L F I G K B J E 2 2. Reflection y = c lines D C H M Return to Questions

72. Penair School Menu x y A L F I G K B J E 2 2. Reflection y = c lines D C H M Return to Questions

73. Penair School Menu x y A L F I G K B J E 2 3. Rotations of 90 o about (0,0) D C H M Return to Questions

74. Penair School Menu x y A L F I G K B J E 2 3. Rotations of 90 o about (0,0) D C H M Return to Questions

75. Penair School Menu x y A L F I G K B J E 2 4. Translations D C H M Return to Questions

76. Penair School Menu x y A L F I G K B J E 2 4. Translations D C H M Return to Questions

77. Penair School Menu x y A L F I G K B J E 2 5. Reflection x = c lines D C H M Return to Questions

78. Penair School Menu x y A L F I G K B J E 2 5. Reflection x = c lines D C H M Return to Questions

79. Penair School Menu 6. Rotations of 180 o x y A L F I G K B J E 2 D C H M Return to Questions

80. Penair School Menu x y A L F I G K B J E 2 6. Rotations of 180 o D C H M Return to Questions

81. Penair School Menu 7. Rotations of 90 o x y A L F I G K B J E 2 D C H M Return to Questions

82. Penair School Menu 7. Rotations of 90 o x y A L F I G K B J E 2 D C H M Return to Questions

83. Penair School Menu 8. Possible “glide reflections” x y A L F I G K B J E 2 D C H M Return to Questions

84. Penair School Menu 8. Possible “glide reflections” x y A L F I G K B J E 2 D C H M Return to Questions

85. Penair School Menu Transformation Challenges Written descriptions only Descriptions and Diagrams Basic translations, reflections + rotations. 123456 123456 123456 Basics + new lines of reflection... More enlargements, centres, SF’s etc.

86. Penair School Menu x y Blue = Object Transformation Challenge A1 Reflect in the y -axis Reflect in the x -axis Translate 6 left and 5 down.

87. Penair School Menu x y Blue = Object Transformation Challenge A2 Translate 0 right and 5 up Reflect in the y -axis Rotate 180 o about (0,0). x

88. Penair School Menu x Blue = Object Transformation Challenge A3 Translate 5 right and 3 down Reflect in the y -axis Rotate - 90 o about (0,0). x y -

89. Penair School Menu x y Blue = Object Transformation Challenge A4 Rotate + 90 o about (0,0) Rotate 180 o about (0,0) Reflect in the y axis x x +

90. Penair School Menu x y Blue = Object Transformation Challenge A5 Translate 6 left and 5 up Rotate 180 o about (3,-2) Reflect in the x axis x

91. Penair School Menu x y Blue = Object Transformation Challenge A6 Rotate 180 o about (0,0) Rotate + 90 o about (0,0) Reflect in the x axis xx +

92. Penair School Menu x y Blue = Object Transformation Challenge B1 Rotate 180 o about (0,-1) Rotate + 90 o about (0,0) Reflect in the line y = - 1 x + x

93. Penair School Menu Transformation Challenge B2 x y Blue = Object Rotate 180 o about (0,0) Rotate + 90 o about (0,0) Rotate 180 o about (-2,0) x xx + x

94. Penair School Menu Transformation Challenge B3 x y Blue = Object Reflect in y = 1 Rotate + 90 o about (1,1) Reflect in the line y = - x (Tricky?) x +

95. Penair School Menu Transformation Challenge B4 x y Blue = Object Reflect in the line x = - 0.5 Reflect in the line y = x Rotate - 90 o about (1,-1) x -

96. Penair School Menu Transformation Challenge B5 Reflect in the line y = x Rotate - 90 o about (-1,0) Reflect in the line y = - x x y Blue = Object x -

97. Penair School Menu Transformation Challenge B6 Rotate 180 o about (-1,-1) Reflect in the line y = x + 1 Enlarge by scale factor + 2, centre (2,4) x y Blue = Object x x

98. Penair School Menu Transformation Challenge C1 Rotate - 90 o about (-4,1) Enlarge by scale factor +0.5 centre (3,-1) Rotate 180 o about (1,0) x y Blue = Object x x - x

99. Penair School Menu Transformation Challenge C2 Rotate 180 o about (-1.5,0.5) Reflect in the line x + y = 2 Enlarge by scale factor + 2, centre (- 5,0) x y Blue = Object x x

100. Penair School Menu Transformation Challenge C3 Enlarge by scale factor + 3, centre (4,5) Rotate 180 o about (-0.5,0.5) Rotate + 90 o about (-1,0) x y Blue = Object x x x +

101. Penair School Menu Transformation Challenge C4 Enlarge by scale factor +0.5, centre (- 5,5) Enlarge by S.F. + 1.5, centre (-1,4) Rotate - 90 o about (3,1) x y Blue = Object x x x -

102. Penair School Menu Transformation Challenge C5 Rotate 180 o centre (-1,0) Enlarge by S.F. + 3, centre (1,- 5) Rotate - 90 o about (2,- 5) x y Blue = Object x x x -

103. Penair School Menu Transformation Challenge C6 Enlarge by scale factor + 2, centre (- 1,4) Rotate - 90 o about (0,- 3) Rotate 180 o about (-1,2.5) x y Blue = Object x x x -