Sarah's Transformation Web
Rotations
Rotations

Rotations

A rotation is a composite of two or more reflections over different intersecting lines.

Examples: (instead of all the points on this face to show the reflections algebraically and arithmetically, the point (6.5,10), which is the point on the top of his head, will be used.)

GEOMETRICALLY

F' is the reflection image under a rotation of 90 degrees. F'' is the reflection image under a rotation of 180 degrees. F''' is the reflection image under a rotation of 270 degrees.

ALGEBRAICALLY

90 degree rotation around the origin
R90 (6.5,10) = (-10,6.5)

180 degree rotation around the origin
R180 (6.5,10) = (-10,-6.5)

270 degree rotation around the origin
R270 (6.5,10) = (10,-6.5)

ARITHMETICALLY

90 degree rotation around the origin

[[0 -1]   *  [[6.5]  =  [[-10]
 [1  0]]       [10]]       [6.5]]

180 degree rotation around the origin

[[-1 0]   *  [[6.5]  =  [[-6.5]
 [0 -1]]       [10]]       [-10 ]]

270 degree rotation around the origin

[[0  1]   *  [[6.5]  =  [[ 10]
[-1 0]]       [10]]       [-6.5]]
NOTE: items usually in subscript will be represented in italics on these pages
by Sarah : turnip@alaska.net -------Last Revised 09/09/96