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Transformations and Tesselations. By: Christine Berg Edited By: VTHamilton. Transformation. Movements of a figure in a plane May be a SLIDE, FLIP, or TURN. Translation. Another name for a SLIDE. A. A’. C. C’. B. B’. A’, B’ and C’ are explained in the next slide. Image.

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Transformations and Tesselations

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Transformations and tesselations l.jpg

Transformationsand Tesselations

By: Christine Berg

Edited By: VTHamilton


Transformation l.jpg

Transformation

  • Movements of a figure in a plane

  • May be a SLIDE, FLIP, or TURN


Translation l.jpg

Translation

Another name for a SLIDE

A

A’

C

C’

B

B’

A’, B’ and C’ are explained in the next slide...


Image l.jpg

Image

The figure you get after a translation

A

A’

Slide

C

B

C’

B’

Image

Original

The symbol ‘ is read “prime”.

ABC has been moved to A’B’C’.

A’B’C’ is the image of ABC.


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Writing a Rule

Finding the amount of movement LEFT and RIGHT and UP and DOWN


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Writing a Rule

Right 4 (positive change in x)

B

Down 3

(negative

change in y)

B’

C

A

A’

C’


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Writing a Rule

Can be written as:

  • R4, D3

    (Right 4, Down 3)

  • (x+4, y-3)


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Reflection

Another name for a FLIP

A

A’

C

B

B’

C’


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Reflection

Used to create SYMMETRY on the coordinate plane


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Symmetry

When one side of a figure is a MIRROR IMAGE of the other


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Line of Reflection

The line you reflect a figure across

Ex: X or Y axis


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Rotation

Another name for a TURN

C’

B’

B

A’

C

A


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Rotation

A transformation that turns about a fixed point


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Center of Rotation

The fixed point

C’

B’

B

A’

C

A

(0,0)


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Rotational Symmetry

When an image after rotation of 180 degrees or less fits exactly on the original


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Rotating a Figure

Measuring the degrees of rotation

C’

B’

B

90 degrees

A’

C

A


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Tessellation

A design that covers a plane with NO GAPS and NO OVERLAPS


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Tessellation

Formed by a combination of TRANSLATIONS, REFLECTIONS, and ROTATIONS


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Pure Tessellation

A tessellation that uses only ONE shape


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Pure Tessellation


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Pure Tessellation


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Semiregular Tessellation

A design that covers a plane using more than one shape


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Semiregular Tessellation


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Semiregular Tessellation


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Semiregular Tessellation


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Semiregular Tessellation


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Tessellation

Used famously in artwork by M.C. Escher


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