Transformationsand Tesselations

By: Christine BergEdited By: VTHamilton

Transformation•Movements of a figure in a plane

•May be a SLIDE, FLIP, or TURN

Translation

Another name for a SLIDE

A

BC

A’

C’ B’

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

ImageThe figure you get after a translation

Original Image

SlideA A’

B B’C C’

The symbol ‘ is read “prime”. ABC has been moved to A’B’C’. A’B’C’ is the image of ABC.

Writing a Rule

Finding the amount of

movement LEFT and RIGHT and UP and DOWN

Writing a Rule9

8

7

6

5

4

3

2

1

0 1 2 3 4 5 6 7 8 9

Right 4 (positive change in x)

Down 3 (negative change in y)

A

A’

B

B’

C

C’

Writing a RuleCan be written as:

•R4, D3(Right 4, Down 3)

•(x+4, y-3)

Reflection

Another name for a FLIP

A A’

C C’B B’

Reflection

Used to create SYMMETRY on the coordinate

plane

Symmetry

When one side of a figure is a

MIRROR IMAGE of the other

Line of Reflection

The line you reflect a figure

acrossEx: X or Y axis

Rotation

Another name for a TURN

B

B’

C

C’

A

A’

Rotation

A transformation that turns about

a fixed point

Center of Rotation

The fixed point

(0,0)

AA’

C

C’

B

B’

Rotational Symmetry

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

Rotating a Figure

Measuring the degrees of

rotation

90 degreesA

A’

C

C’

B

B’

Tessellation

A design that covers a plane with NO GAPS

and NO OVERLAPS

Tessellation

Formed by a combination of TRANSLATIONS, REFLECTIONS,

and ROTATIONS

Pure Tessellation

A tessellation that uses only

ONE shape

Pure Tessellation

Pure Tessellation

Semiregular Tessellation

A design that covers a plane

using more than one shape

Semiregular Tessellation

Semiregular Tessellation

Semiregular Tessellation

Semiregular Tessellation

Tessellation

Used famously in artwork by M.C. Escher