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Transformations y - x x x x
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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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Written descriptions only Descriptions and Diagrams
Transformations Menu Written descriptions only A Translations 1 - 4 5 - 8 B Reflections 1 - 4 5 - 8 C Rotations 1 - 4 5 - 8 D Enlargements 1 - 4 5 - 8 Descriptions and Diagrams A Translations 1 2 3 4 5 6 7 8 B Reflections 1 2 3 4 5 6 7 8 C Rotations 1 2 3 4 5 6 7 8 D Enlargements 1 2 3 4 5 6 7 8 Jungle 1 Question Menu 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 4 5 6
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What is this? Rotation What type of movement does this
picture make you think of? Rotation
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What is this? Reflection
What type of mapping does this picture make you think of? Reflection
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What about this? Enlargement??
What type of mapping does this picture make you think of? Enlargement??
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What is this? Translation
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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Examples of Translations
Use triangle with coordinates (-4 , 0 ) , ( -2 , 0) and ( -4 , 3 ) 1 5 2 Translation of 5 to the right and 2 up 2 7 1 Translation of 7 to the right and 1 up 3 2 Translation of 2 to the right and 2 up 4 5 - 3 Translation of 5 to the right and 3 down
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Examples of Translations
Use triangle with coordinates ( 2 , 0 ) , ( 4 , 0) and ( 2 , 3 ) 5 - 5 Translation of 0 across and 5 down 6 - 4 2 Translation of 4 to the left and 2 up 7 - 5 1 Translation of 5 to the left and 1 up 8 - 6 - 4 Translation of 6 to the left and 4 down
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Examples of Reflections
Use triangle with coordinates (1 , 2 ) , ( 3 , 2) and ( 1 , 5 ) 1 Reflection in the x axis 2 Reflection in the y axis 3 Reflection in the line y = 1 4 Reflection in the line x = - 1
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Examples of Reflections
Use triangle with coordinates ( 3 , 0 ) , ( 5 , 0) and ( 5 , 3 ) 5 Reflection in the line y = x 6 Reflection in the line x = 1.5 7 Reflection in the line y = x - 1 8 Reflection in the line y = - x
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Examples of Rotations 1 2 3 4 Use L- shape with coordinates ( 1 , 0 ),
( 4 , 0), ( 4 , 2 ), ( 3 , 2 ), ( 3 , 1 ) and ( 1 , 1 ) 1 Rotation of + 90o about ( 0 , 0 ) 2 Rotation of + 180o about ( 0 , 0 ) 3 Rotation of - 90o about ( 0 , 0 ) 4 Rotation of + 90o about ( 1 , - 2 )
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Examples of Rotations 5 6 7 8 Use L- shape with coordinates ( 1 , 0 ),
( 4 , 0), ( 4 , 2 ), ( 3 , 2 ), ( 3 , 1 ) and ( 1 , 1 ) 5 Rotation of + 90o about ( 2.5 , 0 ) 6 Rotation of 180o about ( 0 , 1 ) 7 Rotation of - 90o about ( 1 , 0 ) 8 Rotation of + 180o about ( 0 , 2 )
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Examples of Enlargements
1 (-1,-1), (5,-1), (-1,-5) Enlargement of scale factor + 0.5 centre ( - 1 , 5 ) 2 (0,-3), (3,-3), (3,-1) Enlargement of scale factor + 3 centre ( 2 , - 4 ) 3 (-3,2), (0,2), (0,4) Enlargement of scale factor + 2 centre ( - 5 , 3 ) 4 (-1,3), (1,4), (-1,4) Enlargement of scale factor + 5 centre ( 0 , 5 )
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Examples of Enlargements
5 (-1,3), (1,4), (-1,4) Enlargement of scale factor + 5 centre ( 0 , 5 ) 6 (-2,-1), (2,3), (-2,3) Enlargement of scale factor + 0.5 centre ( 4 , - 3 ) 7 (-2,-1), (2,3), (-2,3) Enlargement of scale factor + 0.5 centre ( 4 , - 3 ) 8 (-1,-1), (5,-1), (-1,-5) Enlargement of scale factor + 0.5 centre ( - 1 , 5 )
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A1 y x 5 Translation of 5 to the right and 2 up 2 Blue = Object
Red = Image
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A2 y x 7 Translation of 7 to the right and 1 up 1 Blue = Object
Red = Image
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A3 y x 2 Translation of 2 to the right and 2 up Blue = Object
Red = Image
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A4 y x 5 Translation of 5 to the right and 3 down - 3 Blue = Object
Red = Image
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A5 y x Translation of 0 across and 5 down - 5 Blue = Object
- 5 Translation of 0 across and 5 down x Blue = Object Red = Image
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A6 y x - 4 Translation of 4 to the left and 2 up 2 Blue = Object
Red = Image
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A7 y x - 5 Translation of 5 to the left and 1 up 1 Blue = Object
Red = Image
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A8 y x - 6 Translation of 6 to the left and 2 down - 4 Blue = Object
Red = Image
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B1 y Reflection in the x axis x Blue = Object Red = Image
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B2 y Reflection in the y axis x Blue = Object Red = Image
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B3 y Reflection in the line y = 1 x Blue = Object Red = Image
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B4 y Reflection in the line x = - 1 x Blue = Object Red = Image
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B5 y Reflection in the line y = x x Blue = Object Red = Image
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B6 y Reflection in the line x = 1.5 x Blue = Object Red = Image
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B7 y Reflection in the line y = x - 1 x Blue = Object Red = Image
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B8 y Reflection in the line y = - x x Blue = Object Red = Image
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+ C1 y Rotation of + 90o about ( 0 , 0 ) x Blue = Object Red = Image
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+ C2 y Rotation of + 180o about ( 0 , 0 ) x Blue = Object Red = Image
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+ C3 y Rotation of - 90o about ( 0 , 0 ) x Blue = Object Red = Image
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+ C4 y x Rotation of + 90o about ( 1 , - 2 ) x Blue = Object
Red = Image
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+ C5 y x Rotation of 180o about ( 2.5 , 0 ) x Blue = Object
Red = Image
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+ C6 y Rotation of 180o about ( 0 , 1 ) x x Blue = Object Red = Image
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+ C7 y Rotation of - 90o about ( 1 , 0 ) x x Blue = Object Red = Image
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+ C8 y x x Rotation of + 180o about ( 0 , 2 ) Blue = Object
Red = Image
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D1 y x x (-1,0), (3,2), (-1,2) Enlargement of scale factor + 2
centre ( 1 , 4 ) x Blue = Object Red = Image
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D2 y x (0,-3), (3,-3), (3,-1) Enlargement of scale factor + 3
centre ( 2 , - 4 ) x x Blue = Object Red = Image
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D3 y x x (-3,2), (0,2), (0,4) Enlargement of scale factor + 2
centre ( - 5 , 3 ) x Blue = Object Red = Image
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D4 y x x (-1,3), (1,4), (-1,4) Enlargement of scale factor + 5
centre ( 0 , 5 ) x Blue = Object Red = Image
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D5 y x x (-3,0), (0,0), (0,2) Enlargement of scale factor + 2
centre ( - 5 , 3 ) x Blue = Object Red = Image
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D6 y x (-2,-1), (2,3), (-2,3) Enlargement of scale factor + 0.5
centre ( 4 , - 3 ) x x Blue = Object Red = Image
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D7 y y x x x (-1,1), (-1,-1), (3,1) Enlargement of scale factor + 1.5
centre ( 1 , 5 ) x x Blue = Object Red = Image
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D8 y y x x (-1,-1), (5,-1), (-1,-5) Enlargement of scale factor + 0.5
centre ( - 1 , 5 ) x Blue = Object Red = Image
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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 Question Menu Jungle Question Menu Return to Main Menu
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Transformation Jungle 1
1. Reflection in the y axis 2. Translations 3. Rotations of 180o about (0,0) 4. Reflection in the x axis 5. Rotation of 90o about (0,0) 6. Rotation of 180o about (7,0) 7. Reflections in the x = c lines 8. Possible “glide reflections”
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1. Reflection in the y axis
B D K A F H L I J C G Return to Questions
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1. Reflection in the y axis
B D K A F H L I J C G Return to Questions
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2. Translations x y 1 E B D K A F H L I J C G Return to Questions
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2. Translations x y 1 E B D K A F H L I J C G Return to Questions
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1 E B D K A F H L I J C G 3. Rotations of 180o about (0,0) y x
Return to Questions
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1 E B D K A F H L I J C G 3. Rotations of 180o about (0,0) y x
Return to Questions
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4. Reflection in the x axis
y 1 E B D K A F H L I J C G Return to Questions
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4. Reflection in the x axis
y 1 E B D K A F H L I J C G Return to Questions
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1 E B D K A F H L I J C G 5. Rotations of 90o about (0,0) y x
Return to Questions
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1 E B D K A F H L I J C G 5. Rotations of 90o about (0,0) y x
Return to Questions
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1 E B D K A F H L I J C G 6. Rotation of 180o about (7,0) y x
Return to Questions
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1 E B D K A F H L I J C G 6. Rotation of 180o about (7,0) y x
Return to Questions
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7. Reflection in the x = c lines
y 1 E B D K A F H L I J C G Return to Questions
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7. Reflection in the x = c lines
y 1 E B D K A F H L I J C G Return to Questions
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8. Possible “glide reflections”
x y 1 E B D K A F H L I J C G Return to Questions
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8. Possible “glide reflections”
x y 1 E B D K A F H L I J C G Return to Questions
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Transformation Jungle 2
1. Rotation of 180o about (0,0) 2. Reflections in the y = c lines 3. Rotations of 90o about (0,0) 4. Translations 5. Reflections in the x = c lines 6. Rotations of 180o Rotations of 90o 8. Possible “glide reflections”
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2 B D L F K A H I G C J E M 1. Rotation of 180o about (0,0) y x
Return to Questions
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2 B D L F K A H I G C J E M 1. Rotation of 180o about (0,0) y x
Return to Questions
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2 B D L F K A H I G C J E M 2. Reflection y = c lines y x Return to
Questions
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2 B D L F K A H I G C J E M 2. Reflection y = c lines y x Return to
Questions
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2 B D L F K A H I G C J E M 3. Rotations of 90o about (0,0) y x
Return to Questions
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2 B D L F K A H I G C J E M 3. Rotations of 90o about (0,0) y x
Return to Questions
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4. Translations x y 2 B D L F K A H M I G C J E Return to Questions
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4. Translations x y 2 B D L F K A H M I G C J E Return to Questions
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2 B D L F K A H I G C J E M 5. Reflection x = c lines y x Return to
Questions
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2 B D L F K A H I G C J E M 5. Reflection x = c lines y x Return to
Questions
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2 B D L F K A H I G C J E M 6. Rotations of 180o y x Return to
Questions
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2 B D L F K A H I G C J E M 6. Rotations of 180o y x Return to
Questions
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2 B D L F K A H I G C J E M 7. Rotations of 90o y x Return to
Questions
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2 B D L F K A H I G C J E M 7. Rotations of 90o y x Return to
Questions
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8. Possible “glide reflections”
x y 2 B D L F K A H M I G C J E Return to Questions
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8. Possible “glide reflections”
x y 2 B D L F K A H M I G C J E Return to Questions
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Transformation Challenges
Descriptions and Diagrams Written descriptions 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
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Transformation Challenge A1
y Reflect in the y -axis Reflect in the x -axis x Translate 6 left and 5 down. Blue = Object
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Transformation Challenge A2
y Translate 0 right and 5 up Reflect in the y -axis x x Rotate 180o about (0,0). Blue = Object
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Transformation Challenge A3
y - Translate 5 right and 3 down Reflect in the y -axis x x Rotate - 90o about (0,0). Blue = Object
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Transformation Challenge A4
y Rotate + 90o about (0,0) Rotate 180o Reflect in the y axis + x x x Blue = Object
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Transformation Challenge A5
y Translate 6 left and 5 up Rotate 180o about (3,-2) Reflect in the x axis x x Blue = Object
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Transformation Challenge A6
y Rotate 180o about (0,0) Rotate + 90o Reflect in the x axis + x x x Blue = Object
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Transformation Challenge B1
y Rotate 180o about (0,-1) Rotate + 90o about (0,0) Reflect in the line y = - 1 + x x x Blue = Object
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Transformation Challenge B2
y Rotate 180o about (0,0) Rotate + 90o about (0,0) x x x x x + Rotate 180o about (-2,0) Blue = Object
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Transformation Challenge B3
y + Reflect in y = 1 Rotate + 90o about (1,1) Reflect in the line y = - x (Tricky?) x x Blue = Object
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Transformation Challenge B4
y Reflect in the line x = - 0.5 Reflect in the line y = x - x x Rotate - 90o about (1,-1) Blue = Object
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Transformation Challenge B5
y Reflect in the line y = x Rotate - 90o about (-1,0) line y = - x - x x Blue = Object
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Transformation Challenge B6
y Rotate 180o about (-1,-1) Reflect in the line y = x + 1 Enlarge by scale factor + 2, centre (2,4) x x x Blue = Object
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Transformation Challenge C1
y Rotate - 90o about (-4,1) Enlarge by scale factor +0.5 centre (3,-1) Rotate 180o about (1,0) - x x x x Blue = Object
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Transformation Challenge C2
y Rotate 180o about (-1.5,0.5) Reflect in the line x + y = 2 Enlarge by scale factor + 2, centre (- 5,0) x x x Blue = Object
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Transformation Challenge C3
y + x Enlarge by scale factor + 3, centre (4,5) Rotate 180o about (-0.5,0.5) Rotate + 90o about (-1,0) x x x Blue = Object
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Transformation Challenge C4
y x x Enlarge by scale factor +0.5, centre (- 5,5) S.F , centre (-1,4) Rotate - 90o about (3,1) - x x Blue = Object
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Transformation Challenge C5
y Rotate 180o centre (-1,0) Enlarge by S.F. + 3, centre (1,- 5) Rotate - 90o about (2,- 5) x x - x x Blue = Object
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Transformation Challenge C6
y Enlarge by scale factor + 2, centre (- 1,4) Rotate - 90o about (0,- 3) Rotate 180o about (-1,2.5) x x - x x Blue = Object
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