1. Starter B C D A
Follow the instructions on the starter sheet to transform this trapezium in a variety of ways.

2. Describing Transformations Flow Chart
Yes No
Are the shapes the same size?
Enlargement
Are the shapes the same orientation?
Translation
Can you turn the tracing paper so the shapes look the same?
Rotation
Reflection
Describing Transformations Flow Chart

3. Describe fully the single transformation that maps shape P onto shape Q.
(3 marks)
Enlargement
Scale factor: 2
Centre of enlargement:
(0, 0)
Use the flow chart!

4. Describe fully the single transformation which will map triangle A onto triangle B.
(2 marks)
Reflection
Line of symmetry:
y = x
Use the flow chart!

5. Describe fully the single transformation that maps shape P onto shape Q.
(3 marks)
Rotation
Degrees and direction:
Use the flow chart!

6. Describe fully the single transformation that maps shape P onto shape Q.
(3 marks)
Rotation
Degrees and direction:

7. Describe fully the single transformation that maps shape P onto shape Q.
(3 marks)
Rotation
Degrees and direction:
90° clockwise

8. Describe fully the single transformation that maps shape P onto shape Q.
(3 marks)
Rotation
Degrees and direction:
90° clockwise

9. Describe fully the single transformation that will map shape P onto shape Q.
(2 marks)
Translation
Vector:
3 −1
Use the flow chart!

10. Pair Activity
Match the correct transformation to each diagram which maps the blue shape onto the red shape.

12. Answers
Translated by the vector OR reflected in the line x = 0 (y axis)
Enlarged by scale factor 3 from centre (4, 6)
Rotated 90° clockwise from centre (0, 0)
Translated by the vector −3 −5
Rotated 180° clockwise from centre (0, 0)
Enlarged by scale factor 2 from centre (5, 5)
Translated by the vector 0 5
Reflected in the line y = 1

14. A B C F D E G I H Which shapes are congruent to shape B?
Extension: define congruent.

15. Translation Translation is a type of transformation.
A translation moves an object. The size, shape and orientation stay exactly the same.
We describe translations with a left or right movement (x), followed by an up or down movement (y).

16. 2 -3 Vectors We can use column vectors to describe translations.
This is the x value which tells us the left or right movement.
For example: 2 -3
This is the y value which tells us the up or down movement.

17. Vectors 2 -3
Use axes to help you understand the directions. x y

18. Vectors x y
Use axes to help you understand the directions. x y

19. Describe the translation that maps P onto Q.
a) In words
b) As a vector

20. Describe the translation that maps X onto Y.
a) In words
b) As a vector

21. 4 3 Transform this triangle by the translation:
(4 to the right and 3 up) 4 3

22. 4 3 Transform this triangle by the translation:
(4 to the right and 3 up)
Translate the vertex by the given column vector.
Pick a vertex to begin with. 4 3 3 u P
4 right

23. 4 3 Transform this triangle by the translation:
(4 to the right and 3 up)
Translate the other vertices by the same vector. 4 3

24. 4 3 Transform this triangle by the translation:
(4 to the right and 3 up)
Join the vertices to create the translated shape. 4 3

25. Extension: What word do the translations make?

26. USE VECTORS TO DESCRIBE TRANSLATIONS
Answers
0 −1 −5 − − − − −4
USE VECTORS TO DESCRIBE TRANSLATIONS
MOVE IT

27. Vectors Snakes and Ladders
Roll the dice and move your counter the number of squares shown on the dice.
If you land on a blank numbered square, that ends your go.
If you land on a vector, follow it.
Then it is the end of your go.
The winner is the first person to get to the finish in the exact number of moves.
Printed in DGLs shape box

28. The transformation from A to B is a translation by vector
True or
False?? B 4
The transformation from A to B is a translation by vector 6 A ( ) 6 4
Translation ( ) -6
False -1 28

29. The transformation from A to B is a translation by vector
True or
False?? 5 A 3 B
The transformation from A to B is a translation by vector ( ) -5 -3
Translation ( ) -5
True -3 29

30. The transformation from A to B is a translation by vector
True or
False?? A
The transformation from A to B is a translation by vector ( ) -8
Translation 8 ( ) -8 B
False 30

31. The transformation from A to B is a translation by vector
True or
False?? 6
The transformation from A to B is a translation by vector B A ( ) -6
Translation ( ) -6
True 31

32. Match the images to their reflections
Starter
Match the images to their reflections

33. Match the images to their reflections
Answers
Match the images to their reflections

34. When an object has symmetry, we say it is symmetrical.
When an object does not have symmetry, we say it is asymmetrical.

35. 3 or more lines of symmetry
Asymmetrical
1 line of symmetry
2 lines of symmetry
3 or more lines of symmetry
Categorise the shapes as:
Asymmetrical
1 line of symmetry
2 lines of symmetry
3 or more lines of symmetry

36. 3 or more lines of symmetry
Asymmetrical
1 line of symmetry
2 lines of symmetry
3 or more lines of symmetry

37. What does reflection mean?

38. Reflection Reflection is a type of transformation.
A reflection flips an object. The size and shape stay exactly but the shape is mirrored.
We describe reflections with a line of symmetry.

39. Line of symmetry

40. Line of symmetry

41. Use tracing paper to help you
Line of symmetry
Use tracing paper to help you

42. Draw the object and the line of symmetry on the tracing paper

43. Flip the tracing paper over the line of symmetry

44. Draw over the lines so the pencil transfers over to the paper
Line of symmetry
Draw over the lines so the pencil transfers over to the paper

45. Remove the tracing paper
Line of symmetry
Remove the tracing paper

46. Use tracing paper to help you
Line of symmetry
Use tracing paper to help you

47. Draw the object and the line of symmetry on the tracing paper

48. Flip the tracing paper over the line of symmetry

49. Draw over the lines so the pencil transfers over to the paper
Line of symmetry
Draw over the lines so the pencil transfers over to the paper

50. Remove the tracing paper
Line of symmetry
Remove the tracing paper

52. Swap your sheet with someone near you. Check your partner’s work.
Plenary
Swap your sheet with someone near you.
Check your partner’s work.
Write them a WWW (what went well) and an EBI (even better if) using the keywords below.

53. Starter
How many lines of symmetry do the flags have?

54. Answers
2 1 4
2 2 1
1 0 0
1 2 1
1 0 2

55. Reflection Reflection is a type of transformation.
A reflection flips an object. The size and shape stay exactly but the shape is mirrored.
We describe reflections with a line of symmetry.

56. Transform this triangle by the reflection:10
Transform this triangle by the reflection:
Line y = x 9
Draw the line of symmetry. 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

57. Transform this triangle by the reflection:10
Transform this triangle by the reflection:
Line y = x 9
Flip the shape over the line. 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

58. Transform this triangle by the reflection:10
Transform this triangle by the reflection:
Line y = x 9
You may choose to use tracing paper to make it easier. 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

59. Transform this triangle by the reflection:10
Transform this triangle by the reflection:
Line y = x 9
Place the tracing paper over the top and draw on the line of symmetry and the object. 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

60. Transform this triangle by the reflection:10
Transform this triangle by the reflection:
Line y = x 9
Flip the tracing paper and line up the line of symmetry. 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

61. Transform this triangle by the reflection:10
Transform this triangle by the reflection:
Line y = x 9
Remove the tracing paper and draw the new shape. 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

62. Transform this triangle by the reflection:10
Transform this triangle by the reflection:
Line y = x 9
Remove the tracing paper and draw the new shape. 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

63. Extension: What word do the reflections make?

64. What’s the equation of the line of symmetry?
x = 1

65. What’s the equation of the line of symmetry?

66. What’s the equation of the line of symmetry?
x = 0.5

67. What’s the equation of the line of symmetry?
y = x

69. What do all of these things have in common?
Starter
What do all of these things have in common?

70. The order of rotational symmetry of a shape is determined by how many times the shape fits onto itself during a 360° turn.

71. 3
The order of rotational symmetry of a shape is determined by how many times the shape fits onto itself during a 360° turn. 2 1
ORDER 3

72. 3
The order of rotational symmetry of a shape is determined by how many times the shape fits onto itself during a 360° turn. 2 1
ORDER 3
Every shape has an order of rotational symmetry, even if it is order 1.

73. 3
The order of rotational symmetry of a shape is determined by how many times the shape fits onto itself during a 360° turn. 2 1 1
ORDER 3
Every shape has an order of rotational symmetry, even if it is order 1.
ORDER 1

74. State the order of rotational symmetry for each shape below:

75. Rotation Rotation is a type of transformation.
A rotation turns an object. The size and shape stay exactly the same but the orientation changes.
We describe rotations with an angle, a direction and a centre.

76. Direction - There are two directions when we rotate;
CLOCKWISE &
ANTICLOCKWISE

77. Direction - There are two directions when we rotate;
¼ turn (90°)
½ turn (180°)
¾ turn (270°)
Full turn (360°)
360o
Direction - There are two directions when we rotate;
90o
270o
CLOCKWISE &
ANTICLOCKWISE
180o

78. Rotate this triangle by ¼ turn anticlockwise around A
Use tracing paper to help you! A

79. Rotate this triangle by ¼ turn anticlockwise around A
Draw over the shape. A

80. Rotate this triangle by ¼ turn anticlockwise around A
Draw over the shape. A

81. Rotate this triangle by ¼ turn anticlockwise around A
Draw over the shape. A

82. Rotate this triangle by ¼ turn anticlockwise around A
Use the pencil as a pivot then turn the tracing paper. A

83. Rotate this triangle by ¼ turn anticlockwise around A
Draw in the new shape and remove the tracing paper. A

84. Rotate this rectangle by ½ turn around B
Use tracing paper to help you! B

85. Rotate this rectangle by ½ turn around B
Draw over the shape. B

86. Rotate this rectangle by ½ turn around B
Draw over the shape. B

87. Rotate this rectangle by ½ turn around B
Draw over the shape. B

88. Rotate this rectangle by ½ turn around B
Draw over the shape. B

89. Rotate this rectangle by ½ turn around B
Use the pencil as a pivot then turn the tracing paper. B

90. Rotate this rectangle by ½ turn around B
Draw in the new shape and remove the tracing paper. B

93. Starter Find the order of rotation of these shapes.
Extension: Find the centre of rotation on each of these shapes
Complete these so that they have rotational symmetry about the centre.

94. Answers 2 5 1/None Infinite! 2 3 4 Extension: Get a partner to check!!
2 3 4
Extension: Get a partner to check!!
Get a partner to check!!

95. Rotation Rotation is a type of transformation.
A rotation turns an object. The size and shape stay exactly the same but the orientation changes.
We describe rotations with an angle, a direction and a centre.

96. Transform this triangle by the rotation:10
Transform this triangle by the rotation:
90° clockwise around (4, 5) 9
Identify the centre of rotation. 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

97. Transform this triangle by the rotation:10
Transform this triangle by the rotation:
90° clockwise around (4, 5) 9
Place the tracing paper over the top of the object and centre of rotation. 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

98. Transform this triangle by the rotation:10
Transform this triangle by the rotation:
90° clockwise around (4, 5) 9
Draw the object and the centre of rotation on the tracing paper. 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

99. Transform this triangle by the rotation:10
Transform this triangle by the rotation:
90° clockwise around (4, 5) 9
Put your pencil on the centre of rotation to act as a pivot. 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

100. Transform this triangle by the rotation:10
Transform this triangle by the rotation:
90° clockwise around (4, 5) 9
Hold your pencil still and rotate the tracing paper 90º clockwise. 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

101. Transform this triangle by the rotation:10
Transform this triangle by the rotation:
90° clockwise around (4, 5) 9
Gradually lift the tracing paper and draw the image in its correct place. 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10

102. Extension: What word do the rotations make?

103. Describing Rotations
To describe a rotation we need to know three things:
The angle of the rotation.
For example,
½ turn = 180°
¼ turn = 90°
¾ turn = 270°
The direction of the rotation.
For example, clockwise or anticlockwise.
The centre of rotation.
This is the fixed point about which an object moves.

104. Clockwise or anticlockwise
Answers
Rotation
90° or 180°
Clockwise or anticlockwise
Centre of rotation
A to B
90°
Anticlockwise
(6, 4)
B to C
180° -
(6, 3)
C to D
Clockwise
(0, 3)
D to E
(0, -2)
E to F
(-1, -6)
F to G
(3, -8)
G to H
(-7, 3)
H to I
(-3, 6)
I to A
(1, 4)