TOTALLY TRANSFORMED

Using Cabri Jr. on the TI-83 or 84

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

WHAT ARE THE THREE TYPES OF RIGID TRANSFORMATIONS?

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

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

WHAT TYPE OF TRANSFORMATION WAS ILLUSTRATED IN THE PICTURE?

1. Rotation2. Reflection3. Translation

WHAT TYPE OF TRANSFORMATION WAS ILLUSTRATED IN THE PICTURE?

1. Rotation2. Reflection3. 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 cursora

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 GAMEPlayer 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 90Rotate bottom

right 90

To create Stage 3 repeat the process

STAGE Number of Tiles

0 11 32 93 27? ?

What are some examples of transformations in the real

world?