Transformations - MathInScience.info.

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Transcript Transformations - MathInScience.info.

Transformations

MathScience Innovation Center Betsey Davis

Transformation= change



Isometry



Translation



Reflection

–

Over a line

Copy these down and skip lines to keep notes.

Notes graded today !

–

Around a point

–

Lines of Symmetry



Dilation

Transformations B. Davis 2005 MathScience Innovation Center

Isometry

 Change that preserves lengths and angle measures Example: isometric Example: Not isometric Transformations B. Davis 2005 MathScience Innovation Center

Isometry

 Isometry or not?

NOT !

Transformations B. Davis 2005 MathScience Innovation Center

Translations

By: Alisa

Use the tip of the cow’s ear as the starting point (0,4) -10 -5 By: Alisa -8 -6 -2 -4 8 6 4 2 5 10

Translated up New equation: f(x)+4 -10 -5 By: Alisa -8 -6 -2 -4 8 6 4 2 5 Original f(x) 10

Translation = slip or slide

 Up  Down  Right  Left Transformations B. Davis 2005 MathScience Innovation Center

-10 -5 Translated down New equation: f(x)-6 -2 -4 -6 -8 8 6 4 2 Original f(x) 5 10

-10 -5 Translated left -2 -4 New equation: f(x+7) -6 -8 8 6 4 2 5 10 Original f(x)

-10 -5 8 6 4 2 -6 -8 5 -4 -2 Original f(x) Translated right 10 New equation: f(x-8)

Transformations B. Davis 2005 MathScience Innovation Center

By Camille 2 -5 -2 Transformations B. Davis 2005 MathScience Innovation Center 5

Reflection over a line: Flip

 Up and down  Left and right Transformations B. Davis 2005 MathScience Innovation Center

By Camille 2 -5 -2 Transformations B. Davis 2005 MathScience Innovation Center 5

2 -5 -2 By Camille Transformations B. Davis 2005 MathScience Innovation Center 5

Reflection about a point= rotation

 Rather than flip over a line Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point= rotation

 Rather than flip over a line Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point= rotation

 Rather than flip over a line-

Line Reflection

The line is called the line

Reflection about a point= rotation

 Rather than flip over a line  Spin about a point

Line Reflection

Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point= rotation

 Rather than flip over a line  Spin about a point

Line Reflection

Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point= rotation

 Rather than flip over a line  Spin about a point

Line Reflection

Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point = rotation

 30 degrees  90 degrees  180 degrees  ¾ of a turn Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point = rotation

 30 degrees  90 degrees  180 degrees  ¾ of a turn Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point = rotation

 30 degrees  90 degrees  180 degrees  ¾ of a turn Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point = rotation

 30 degrees  90 degrees  180 degrees  ¾ of a turn Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point = rotation

 30 degrees  90 degrees  180 degrees  ¾ of a turn Transformations B. Davis 2005 MathScience Innovation Center

Reflection about a point = rotation

 30 degrees  90 degrees  180 degrees  ¾ of a turn Transformations B. Davis 2005 MathScience Innovation Center

Refection:

 Over line  About a point Transformations B. Davis 2005 MathScience Innovation Center

Refection:

 Over line  About a point Transformations B. Davis 2005 MathScience Innovation Center

Refection:

 Over line  About a point Transformations B. Davis 2005 MathScience Innovation Center

Refection:

 Over line  About a point Transformations B. Davis 2005 MathScience Innovation Center

Refection:

 Over line  About a point Transformations B. Davis 2005 MathScience Innovation Center

Refection:

 Over line  About a point Transformations B. Davis 2005 MathScience Innovation Center

Refection:

 Over line  About a point Transformations B. Davis 2005 MathScience Innovation Center

Lines of Symmetry

 To count lines of symmetry, imagine how many times you can rotate image and match original Example: a square has 4 lines of symmetry but a rectangle only has 2 Transformations B. Davis 2005 MathScience Innovation Center

Lines of Symmetry

 To count lines of symmetry, imagine how many times you can rotate image and match original Example: How many lines does a regular pentagon have?

Example: How many lines does a non-regular pentagon have?

Transformations B. Davis 2005 MathScience Innovation Center

By: Stephanie Hill

-10 -5 By: Stephanie Hill -6 -2 -4 8 6 4 2 5 10

Dilation: Stretch or Shrink

 Vertically: taller or shorter  Horizontally: fatter or skinnier Transformations B. Davis 2005 MathScience Innovation Center

-10 -5 By: Stephanie -2 -4 -6 8 6 4 2 5 10

-10 -5 By: Stephanie Hill -6 -2 -4 8 6 4 2 5 10

-10 -5 By: Stephanie -2 -4 -6 8 6 4 2 5 10

Transformation= change



Isometry



Translation



Reflection

–

Over a line

–

Around a point

Hopefully you have notes now on all of this.

We add one more item now.

Notes graded today !

–

Lines of Symmetry



Dilation

Transformations B. Davis 2005 MathScience Innovation Center

Tessellation



Completely covering a plane with shapes with

–

No overlapping

–

No gaps

Here is one more.

Notes graded today !

Transformations B. Davis 2005 MathScience Innovation Center

Tessellation

M 2 W 2 X 6 2 U 2 D K 2 10 I B 7 K 2 5 W 6 Y 2 T 6 I C 4 7 5 M 6 X Z 4 2 R I 11 R J 5 E G 12 10 E F 3 4 D 4 6 2 S Y 4 6 Transformations B. Davis 2005 MathScience Innovation Center 11 Y 1 G 3 5 2 C 3 F 7 2 B 2 10 L I M E 1 11 B 1 10 I G 6 6 I E F 6 1 Z O 2 9 J 6 J 10

F 6 I 7 P 5 O 5 V 5 1 R 5 S 5 1 S 5 Q 7 5 T 5 6 G 7 1 B D 7 1 C 6 H 6 7 E 5 1 C 7 1 1 V 6 6 K 6 1 T A 5 E 7 4 I 6 7 G 6 1 Z J D 6 6 L 2 M 6 1 E 5 C 5 P R 6 5 2 Transformations B. Davis 2005 MathScience Innovation Center 5 K 5 2 R 6 1 T E 5 2 X J 6 1 A 6 1 2 P 1 M 1 T F 2 Z 4 U 1 I 3 P 1 J 1 I 1 S V 4 3 2

http://www.learnalberta.ca/Math/ math6web/math6shell.swf

This website reviews translations and line reflections.

http://michaelshepperd.tripod.com/resources/tessellations.html

This website shows tessellations.

Transformations B. Davis 2005 MathScience Innovation Center

Geometry in Art

 Time to practice!

Rotation Or reflection about a point translation translation Transformations B. Davis 2005 MathScience Innovation Center