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TOTALLY TRANSFORMED
Using Cabri Jr. on the TI-83 or 84
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WHAT HAPPENS IN A RIGID
TRANSFORMATION
1.The shape changes size and position
2.The shape changes size but not position
3.The shape changes position but not size
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WHAT ARE THE THREE TYPES OF RIGID TRANSFORMATIONS?
1. Rotation, Reduction, Reflection
2. Translation, Reflection, Dilation
3. Rotation, Reflection, Translation
4. Reflection, Rotation, Dilation
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WHAT TYPE OF TRANSFORMATION WAS ILLUSTRATED IN THE PICTURE?
1. Rotation
2. Reflection
3. Translation
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WHAT TYPE OF TRANSFORMATION WAS ILLUSTRATED IN THE PICTURE?
1. Rotation
2. Reflection
3. Translation
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WHAT TYPE OF TRANSFORMATION WAS ILLUSTRATED IN THE PICTURE?
1. Rotation
2. Reflection
3. Translation
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• Discover what happens in each type of transformation.
• Use graphing calculators to make our discoveries
• Create fractals using transformations
TODAY WE WILL……
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CABRI JR.IMPORTANT KEYS
∏π∫ª º
Arrows move the cursor
a
AU
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LETS PRACTICE
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• Follow the directions on your sheet
• Record all measurements in journal
• Determine a definition
• Draw an illustration
NOW IT’S YOUR TURN
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RECORD INFORMATION IN YOUR JOURNAL
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WHAT DID WE DISCOVER?
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Distance: A,A’ _____
B,B’ _____
C,C’ _____
Dragging the point what happened?
TRANSLATION
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A transformation that _______ each point of a figure the same _________ and in the same _______ .
TRANSLATIONslides
distancedirection
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CAN YOU FIND A TRANSLATION IN THE TILE?
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•Distance: A,A’: _____ B,B’: _____
C,C’: _____
ROTATION
•ANGLES: <ADA’: _____ <BDB’: _____
<CDC’: _____
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A transformation that _______ a figure ________ a point. The angle measurement between ____________________
and the _________________
are the _____.
ROTATIONturns
aroundcorresponding pointscenter of rotationsame
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CAN YOU FIND A ROTATION IN THE TILE?
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LETS CREATE THE REFLECTION TOGETHER
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•Distance: A,A’: _____ B,B’: _____
C,C’: _____
REFLECTION
•ANGLES: <ADA’: _____ <BDB’: _____
<CDC’: _____
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REFLECTIONA transformation that _____ a figure across the line of _________ forming a _____________ bisector with the segment joining the ___________________.
flipsreflection perpendicular
corresponding points
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CAN YOU FIND A REFLECTION IN THE TILE?
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TRANSFORMATION GAME
Player 1 spins and arrow lands on red
a. Look at keyb. Reflect up one blockc. Rotate 90 counter- clockwised. Translate diagonally
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FRACTAL TILES
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• Geometric figures built up from a simple shape by repeating the same changes at smaller and smaller scales. (recursion)
WHAT ARE FRACTALS?
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• Self-similar objects that look the same no matter to what stage you zoom.
WHAT ARE FRACTALS?
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FRACTALS CAN BE FOUND IN …
MOVIES TECHNOLOGYARCHITECHTURE
NATURE
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Creating stage 1 Translation
Translate
one tile up
Translate
one tile right
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Creating stage 1 Rotation
Rotate the top 90 degrees clockwise
Rotate the bottom right 90 degrees clockwise
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Creating stage 2 Translation Translate one grid
up and one grid to the right
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Rotate top 90
Rotate bottom right 90
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To create Stage 3 repeat the process
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STAGE Number of Tiles
0 1
1 3
2 9
3 27
? ?
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What are some examples of transformations in the real
world?