Transformations and Tessellations Edited By: K. Stone.

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Presentation transcript:

Transformations and Tessellations Edited By: K. Stone

Transformation Movements of a figure in a plane May be a SLIDE, FLIP, or TURN

Translation Another name for a SLIDE A B C A’ C’ B’ A’, B’ and C’ are explained in the next slide...

Image The figure you get after a translation Original Image Slide AA’ BB’CC’ 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 Rule Right 4 (positive change in x) Down 3 (negative change in y) A A’ B B’ C C’

Writing a Rule Can be written as: R4, D3 (Right 4, Down 3) (x+4, y-3)

Reflection Another name for a FLIP AA’ CC’BB’

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 across Ex: 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) A A’ 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 degrees A 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

Semiregular Tessellation A design that covers a plane using more than one shape

Semiregular Tessellation

What will tessellate? In order to tessellate, shapes must fit together to form 360 ○ at their vertex. To find out if a shape will tessellate a plane alone, divide the measure of one of its angles into 360. If it divides evenly, it will tessellate. If not, it won’t. For example, a square has 90 ○ angles. 90 goes into 360 exactly 4 times, so a square will tessellate by itself.

Tessellation Used famously in artwork by M.C. Escher

LINKS Cool math Lessons - Geometry - What are Tessellations?Cool math Lessons - Geometry - What are Tessellations? Interactivate: Tessellate!