Transformations
y
x
-
x
x
x
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Penair School
Transformations
Menu
1. Examples of different Transformation
Individual transformations explained plus sets
of four descriptions to draw.
2. Transformation “Jungles”
Questions on diagrams containing a large
number of shapes. List the shapes that fit.
3. Predicting Activity (Three levels)
Questions on diagrams containing a large
number of shapes. List the shapes that fit.
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Penair School
Transformations Menu
Written descriptions only
A
B
C
D
Translations
Reflections
Rotations
Enlargements
1-4
1-4
1-4
1-4
5-8
5-8
5-8
5-8
Descriptions and Diagrams
A
B
C
D
Translations
Reflections
Rotations
Enlargements
1
1
1
1
2
2
2
2
3
3
3
3
Jungle 1 Question Menu
4
4
4
4
5
5
5
5
6
6
6
6
7
7
7
7
8
8
8
8
Jungle 2. Question Menu
Basic translations, reflections + rotations.
1 2 3 4 5 6
Basics + new lines of reflection ...
1 2 3 4 5 6
More enlargements, centres, SF’s etc.
1 2 3 Menu
4 5 6
Penair School
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Penair School
What is this?
What type of movement does this
picture make you think of?
Rotation
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What is this?
What type of mapping does this
picture make you think of?
Reflection
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What about this?
What type of mapping does this
picture make you think of?
Enlargement??
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What is this?
What type of mapping does this
picture make you think of?
Translation
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Examples of Transformations
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.
Written descriptions only
Descriptions and Diagrams
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Penair School
Examples of Translations
Use triangle with coordinates (-4 , 0 ) ,
( -2 , 0) and ( -4 , 3 )
1 Translation of
5
2
2
5 to the right
and 2 up
3 Translation of
2 to the right
and 2 up
7
1
Translation of
7 to the right
and 1 up
2
2
4
Translation of
5
-3
5 to the right
and 3 down
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Penair School
Examples of Translations
Use triangle with coordinates ( 2 , 0 ) ,
( 4 , 0) and ( 2 , 3 )
5 Translation of
0
-5
6
0 across
and 5 down
7
Translation of
5 to the left
and 1 up
Translation of
-4
2
4 to the left
and 2 up
-5
1
8
Translation of
-6
-4
6 to the left
and 4 down
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Penair School
Examples of Reflections
Use triangle with coordinates (1 , 2 ) ,
( 3 , 2) and ( 1 , 5 )
1
3
Reflection in
the x axis
Reflection in
the line y = 1
2
4
Reflection in
the y axis
Reflection in
the line x = - 1
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Penair School
Examples of Reflections
Use triangle with coordinates ( 3 , 0 ) ,
( 5 , 0) and ( 5 , 3 )
5
7
Reflection in
the line y = x
Reflection in
the line y = x - 1
6
8
Reflection in
the line x = 1.5
Reflection in
the line y = - x
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Penair School
Examples of Rotations
Use L- shape with coordinates ( 1 , 0 ),
( 4 , 0), ( 4 , 2 ), ( 3 , 2 ), ( 3 , 1 ) and ( 1 , 1 )
1
3
Rotation of + 90o
about ( 0 , 0 )
Rotation of about ( 0 , 0 )
90o
2
4
Rotation of + 180o
about ( 0 , 0 )
Rotation of + 90o
about ( 1 , - 2 )
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Penair School
Examples of Rotations
Use L- shape with coordinates ( 1 , 0 ),
( 4 , 0), ( 4 , 2 ), ( 3 , 2 ), ( 3 , 1 ) and ( 1 , 1 )
5
7
90o
6
90o
8
Rotation of +
about ( 2.5 , 0 )
Rotation of about ( 1 , 0 )
Rotation of 180o
about ( 0 , 1 )
Rotation of + 180o
about ( 0 , 2 )
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Examples of Enlargements
1
3
(-1,-1), (5,-1), (-1,-5) 2
Enlargement of
scale factor + 0.5
centre ( - 1 , 5 )
(-3,2), (0,2), (0,4)
Enlargement of
scale factor + 2
centre ( - 5 , 3 )
4
(0,-3), (3,-3), (3,-1)
Enlargement of
scale factor + 3
centre ( 2 , - 4 )
(-1,3), (1,4), (-1,4)
Enlargement of
scale factor + 5
centre ( 0 , 5 )
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Penair School
Examples of Enlargements
5
7
(-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 )
6
8
(-2,-1), (2,3), (-2,3)
Enlargement of
scale factor + 0.5
centre ( 4 , - 3 )
(-1,-1), (5,-1), (-1,-5)
Enlargement of
scale factor + 0.5
centre ( - 1 , 5 )
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A1
y
5
2
Translation of
x
Blue
Red
=
=
Object
Image
5 to the right
and 2 up
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A2
y
7
1
Translation of
x
Blue
Red
=
=
Object
Image
7 to the right
and 1 up
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A3
y
2
2
Translation of
x
Blue
Red
=
=
Object
Image
2 to the right
and 2 up
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A4
y
Translation of
x
Blue
Red
=
=
Object
Image
5
-3
5 to the right
and 3 down
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A5
y
Translation of
x
Blue
Red
=
=
Object
Image
0
-5
0 across
and 5 down
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A6
y
Translation of
x
Blue
Red
=
=
Object
Image
-4
2
4 to the left
and 2 up
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A7
y
Translation of
x
Blue
Red
=
=
Object
Image
-5
1
5 to the left
and 1 up
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A8
y
Translation of
x
Blue
Red
=
=
Object
Image
-6
-4
6 to the left
and 2 down
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B1
y
x
Blue
Red
=
=
Object
Image
Reflection in
the x axis
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B2
y
x
Blue
Red
=
=
Object
Image
Reflection in
the y axis
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B3
y
x
Blue
Red
=
=
Object
Image
Reflection in
the line y = 1
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B4
y
x
Blue
Red
=
=
Object
Image
Reflection in
the line x = - 1
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B5
y
x
Blue
Red
=
=
Object
Image
Reflection in
the line y = x
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B6
y
x
Blue
Red
=
=
Object
Image
Reflection in
the line x = 1.5
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B7
y
x
Blue
Red
=
=
Object
Image
Reflection in
the line y = x - 1
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B8
y
x
Blue
Red
=
=
Object
Image
Reflection in
the line y = - x
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+
C1
y
x
Blue
Red
=
=
Object
Image
Rotation of + 90o
about ( 0 , 0 )
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+
C2
y
x
Blue
Red
=
=
Object
Image
Rotation of + 180o
about ( 0 , 0 )
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+
C3
y
x
Blue
Red
=
=
Object
Image
Rotation of - 90o
about ( 0 , 0 )
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+
C4
y
x
Rotation of + 90o
about ( 1 , - 2 )
x
Blue
Red
=
=
Object
Image
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+
C5
y
x
Blue
Red
=
=
Object
Image
x
Rotation of 180o
about ( 2.5 , 0 )
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+
C6
y
x
x
Blue
Red
=
=
Object
Image
Rotation of 180o
about ( 0 , 1 )
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+
C7
y
x
Blue
Red
=
=
Object
Image
x
Rotation of - 90o
about ( 1 , 0 )
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+
C8
y
x
x
Blue
Red
=
=
Object
Image
Rotation of + 180o
about ( 0 , 2 )
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D1
y
x
x
Blue
Red
=
=
Object
Image
(-1,0), (3,2), (-1,2)
Enlargement of
scale factor + 2
centre ( 1 , 4 )
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D2
y
x
(0,-3), (3,-3), (3,-1)
Enlargement of
scale factor + 3
centre ( 2 , - 4 )
x
Blue
Red
=
=
Object
Image
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D3
y
x
x
Blue
Red
=
=
Object
Image
(-3,2), (0,2), (0,4)
Enlargement of
scale factor + 2
centre ( - 5 , 3 )
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D4
x
y
x
Blue
Red
=
=
Object
Image
(-1,3), (1,4), (-1,4)
Enlargement of
scale factor + 5
centre ( 0 , 5 )
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D5
y
x
x
Blue
Red
=
=
Object
Image
(-3,0), (0,0), (0,2)
Enlargement of
scale factor + 2
centre ( - 5 , 3 )
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D6
y
x
(-2,-1), (2,3), (-2,3)
Enlargement of
scale factor + 0.5
centre ( 4 , - 3 )
x
Blue
Red
=
=
Object
Image
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Penair School
D7
y
x
x
Blue
Red
=
=
Object
Image
(-1,1), (-1,-1), (3,1)
Enlargement of
scale factor + 1.5
centre ( 1 , 5 )
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D8
x
y
x
Blue
Red
=
=
Object
Image
(-1,-1), (5,-1), (-1,-5)
Enlargement of
scale factor + 0.5
centre ( - 1 , 5 )
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Transformation “Jungles”
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.
Jungle 1.
Jungle 2.
Question Menu
Question Menu
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Penair School
1
Transformation Jungle 1
1.
2.
3.
4.
5.
6.
7.
8.
Reflection in the y axis
Translations
Rotations of 180o about (0,0)
Reflection in the x axis
Rotation of 90o about (0,0)
Rotation of 180o about (7,0)
Reflections in the x = c lines
Possible “glide reflections”
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1.
Reflection in the y axis
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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1.
Reflection in the y axis
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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2.
Translations
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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2.
Translations
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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3. Rotations of 180o about (0,0)
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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3. Rotations of 180o about (0,0)
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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4.
Reflection in the x axis
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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4.
Reflection in the x axis
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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5. Rotations of 90o about (0,0)
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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5. Rotations of 90o about (0,0)
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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6. Rotation of 180o about (7,0)
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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6. Rotation of 180o about (7,0)
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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7. Reflection in the x = c lines
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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7. Reflection in the x = c lines
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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8. Possible “glide reflections”
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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8. Possible “glide reflections”
y
1
E
B
D
K
H
A
F
L
I
J
C
G
x
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2
Transformation Jungle 2
1.
2.
3.
4.
5.
6.
7.
8.
Rotation of 180o about (0,0)
Reflections in the y = c lines
Rotations of 90o about (0,0)
Translations
Reflections in the x = c lines
Rotations of 180o
Rotations of 90o
Possible “glide reflections”
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1. Rotation of 180o about (0,0)
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
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1. Rotation of 180o about (0,0)
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
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2. Reflection y = c lines
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
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2. Reflection y = c lines
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
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3. Rotations of 90o about (0,0)
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
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3. Rotations of 90o about (0,0)
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
Return to
Questions
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4. Translations
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
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4. Translations
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
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5. Reflection x = c lines
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
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5. Reflection x = c lines
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
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6. Rotations of 180o
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
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Questions
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6.
Rotations of 180o
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
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Questions
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7.
Rotations of 90o
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
Return to
Questions
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7. Rotations of 90o
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
Return to
Questions
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8. Possible “glide reflections”
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
Return to
Questions
Menu
Penair School
8. Possible “glide reflections”
y
2
L
B
D
F
K
H
A
M
I
J
E
x
G
C
Return to
Questions
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Transformation Challenges
Descriptions
Written descriptions
and Diagrams
only
Basic translations, reflections + rotations.
1 2 3 4 5 6
Basics + new lines of reflection ...
1 2 3 4 5 6
More enlargements, centres, SF’s etc.
1 2 3 4 5 6
Menu
Penair School
Transformation Challenge A1
y
Reflect in the
y -axis
x
Reflect in the
x -axis
Translate 6 left
and 5 down.
Blue
=
Object
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Penair School
Transformation Challenge A2
y
x
Translate 0 right
and 5 up
x
Reflect in the
y -axis
Rotate 180o
about (0,0).
Blue
=
Object
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Transformation Challenge A3
-
y
x
Translate 5 right
and 3 down
x
Reflect in the
y -axis
Rotate - 90o
about (0,0).
Blue
=
Object
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Transformation Challenge A4
y
Rotate + 90o
about (0,0)
+
x
x
Rotate 180o
about (0,0)
Reflect in the
y axis
Blue
=
Object
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Transformation Challenge A5
y
Translate 6 left
and 5 up
x
Rotate 180o
about (3,-2)
x
Reflect in the
x axis
Blue
=
Object
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Transformation Challenge A6
y
Rotate 180o
about (0,0)
+
x
x
Rotate + 90o
about (0,0)
Reflect in the
x axis
Blue
=
Object
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Transformation Challenge B1
y
Rotate 180o
about (0,-1)
+
x
x
x
Rotate + 90o
about (0,0)
Reflect in the
line y = - 1
Blue
=
Object
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Transformation Challenge B2
y
x
x
+
Blue
=
Rotate 180o
about (0,0)
x
Rotate + 90o
about (0,0)
Rotate 180o
about (-2,0)
Object
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Transformation Challenge B3
y
+
Reflect in y = 1
x
x
Blue
=
Object
Rotate + 90o
about (1,1)
Reflect in the
line y = - x
(Tricky?)
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Transformation Challenge B4
y
Reflect in the
line x = - 0.5
x
-
x
Reflect in the
line y = x
Rotate - 90o
about (1,-1)
Blue
=
Object
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Transformation Challenge B5
y
x
Reflect in the
line y = x
-
x
Rotate - 90o
about (-1,0)
Reflect in the
line y = - x
Blue
=
Object
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Transformation Challenge B6
y
Rotate 180o
about (-1,-1)
x
x
x
Blue
=
Object
Reflect in the
line y = x + 1
Enlarge by
scale factor + 2,
centre (2,4)
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Transformation Challenge C1
y
x
-
Rotate - 90o
about (-4,1)
x
x
x
Enlarge by
scale factor +0.5
centre (3,-1)
Rotate 180o
about (1,0)
Blue
=
Object
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Transformation Challenge C2
y
x
Blue
x
=
Rotate 180o
about (-1.5,0.5)
x
Object
Reflect in the
line x + y = 2
Enlarge by
scale factor + 2,
centre (- 5,0)
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Transformation Challenge C3
y
+
x
x
Enlarge by
scale factor + 3,
centre (4,5)
x
x
Rotate 180o
about (-0.5,0.5)
Rotate + 90o
about (-1,0)
Blue
=
Object
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Transformation Challenge C4
x
x
y
-
Enlarge by
scale factor +0.5,
centre (- 5,5)
x
x
Enlarge by
S.F. + 1.5,
centre (-1,4)
Rotate - 90o
about (3,1)
Blue
=
Object
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Transformation Challenge C5
y
Rotate 180o
centre (-1,0)
x
x
-
x x
Blue
=
Enlarge by
S.F. + 3,
centre (1,- 5)
Rotate - 90o
about (2,- 5)
Object
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Transformation Challenge C6
y
Enlarge by
scale factor + 2,
centre (- 1,4)
x
x
-
x
Rotate - 90o
about (0,- 3)
x
Rotate 180o
about (-1,2.5)
Blue
=
Object
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