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TOTALLY TRANSFORMED
Using Cabri Jr. on the TI-83 or 84
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
WHAT ARE THE THREE TYPES OF RIGID TRANSFORMATIONS?
1. Rotation, Reduction, Reflection
2. Translation, Reflection, Dilation
3. Rotation, Reflection, Translation
4. Reflection, Rotation, Dilation
WHAT TYPE OF TRANSFORMATION WAS ILLUSTRATED IN THE PICTURE?
1. Rotation
2. Reflection
3. Translation
WHAT TYPE OF TRANSFORMATION WAS ILLUSTRATED IN THE PICTURE?
1. Rotation
2. Reflection
3. Translation
WHAT TYPE OF TRANSFORMATION WAS ILLUSTRATED IN THE PICTURE?
1. Rotation
2. Reflection
3. Translation
• Discover what happens in each type of transformation.
• Use graphing calculators to make our discoveries
• Create fractals using transformations
TODAY WE WILL……
CABRI JR.IMPORTANT KEYS
∏π∫ª º
Arrows move the cursor
a
AU
LETS PRACTICE
• Follow the directions on your sheet
• Record all measurements in journal
• Determine a definition
• Draw an illustration
NOW IT’S YOUR TURN
RECORD INFORMATION IN YOUR JOURNAL
WHAT DID WE DISCOVER?
Distance: A,A’ _____
B,B’ _____
C,C’ _____
Dragging the point what happened?
TRANSLATION
A transformation that _______ each point of a figure the same _________ and in the same _______ .
TRANSLATIONslides
distancedirection
CAN YOU FIND A TRANSLATION IN THE TILE?
•Distance: A,A’: _____ B,B’: _____
C,C’: _____
ROTATION
•ANGLES: <ADA’: _____ <BDB’: _____
<CDC’: _____
A transformation that _______ a figure ________ a point. The angle measurement between ____________________
and the _________________
are the _____.
ROTATIONturns
aroundcorresponding pointscenter of rotationsame
CAN YOU FIND A ROTATION IN THE TILE?
LETS CREATE THE REFLECTION TOGETHER
•Distance: A,A’: _____ B,B’: _____
C,C’: _____
REFLECTION
•ANGLES: <ADA’: _____ <BDB’: _____
<CDC’: _____
REFLECTIONA transformation that _____ a figure across the line of _________ forming a _____________ bisector with the segment joining the ___________________.
flipsreflection perpendicular
corresponding points
CAN YOU FIND A REFLECTION IN THE TILE?
TRANSFORMATION GAME
Player 1 spins and arrow lands on red
a. Look at keyb. Reflect up one blockc. Rotate 90 counter- clockwised. Translate diagonally
FRACTAL TILES
• Geometric figures built up from a simple shape by repeating the same changes at smaller and smaller scales. (recursion)
WHAT ARE FRACTALS?
• Self-similar objects that look the same no matter to what stage you zoom.
WHAT ARE FRACTALS?
FRACTALS CAN BE FOUND IN …
MOVIES TECHNOLOGYARCHITECHTURE
NATURE
Creating stage 1 Translation
Translate
one tile up
Translate
one tile right
Creating stage 1 Rotation
Rotate the top 90 degrees clockwise
Rotate the bottom right 90 degrees clockwise
Creating stage 2 Translation Translate one grid
up and one grid to the right
Rotate top 90
Rotate bottom right 90
To create Stage 3 repeat the process
STAGE Number of Tiles
0 1
1 3
2 9
3 27
? ?
What are some examples of transformations in the real
world?