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.)

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

R*90* (6.5,10) = (-10,6.5)

180 degree rotation around the origin

R*180* (6.5,10) = (-10,-6.5)

270 degree rotation around the origin

R*270* (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]]

- Return to Transformations,
- Reflections
- Translations
- Scale Changes

by Sarah : turnip@alaska.net -------Last Revised 09/09/96