Totally Transformed

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TOTALLY TRANSFORMED Using Cabri Jr. on the TI-83 or 84

description

Totally Transformed. Using Cabri Jr. on the TI-83 or 84. The shape changes size and position The shape changes size but not position The shape changes position but not size . What happens In a rigid transformation. Rotation, Reduction, Reflection Translation, Reflection, Dilation - PowerPoint PPT Presentation

Transcript of Totally Transformed

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TOTALLY TRANSFORMED

Using Cabri Jr. on the TI-83 or 84

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WHAT HAPPENS IN A RIGID

TRANSFORMATION1.The shape changes size and

position2.The shape changes size but not

position3.The shape changes position but not

size

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WHAT ARE THE THREE TYPES OF RIGID TRANSFORMATIONS?

1. Rotation, Reduction, Reflection2. Translation, Reflection, Dilation3. Rotation, Reflection, Translation4. Reflection, Rotation, Dilation

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WHAT TYPE OF TRANSFORMATION WAS ILLUSTRATED IN THE PICTURE?1. Rotation2. Reflection3. Translation

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WHAT TYPE OF TRANSFORMATION WAS ILLUSTRATED IN THE PICTURE?

1. Rotation2. Reflection3. Translation

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WHAT TYPE OF TRANSFORMATION WAS ILLUSTRATED IN THE PICTURE?

1. Rotation2. Reflection3. 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 cursora

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 GAMEPlayer 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 90Rotate bottom

right 90

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To create Stage 3 repeat the process

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STAGE Number of Tiles

0 11 32 93 27? ?

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What are some examples of transformations in the real

world?