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
B
C‟
B‟
A‟, B‟ and C‟ are explained in the next slide...
Image
The figure you get after a translation A A‟
Slide
C
Original
B
C‟
Image
B‟
The symbol „ is read “prime”. ABC has been moved to A‟B‟C‟.
Writing a Rule Finding the amount of movement LEFT and RIGHT and UP and DOWN
Writing a Rule
9 8
7
B
Right 4 (positive change in x)
6 5
4
A
B‟ C
Down 3 (negative change in y)
3 2 1
0 1 2 3
A‟
4
5
6
7
C‟
8
9
Writing a Rule Can be written as: •R4, D3 (Right 4, Down 3) •(x+4, y-3)
Reflection Another name for a FLIP
A A‟
C
B
B‟
C‟
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
C‟
B‟
B
A‟
C
A
Rotation A transformation that turns about a fixed point
Center of Rotation The fixed point
C‟ B‟
B
C
A‟ A
(0,0)
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
C‟
B‟ B
A‟ C
A
90 degrees
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