Rotation
Pronunciation: /roʊˈteɪ.ʃən/ Explain
Click on the green point on the slider and drag it to rotate the object. Click on the blue points and drag them to change the figure.
At what angles of rotation is the rotated object exactly on top of the original object?
 Manipulative 1  Rotation Created with GeoGebra. 

A rotation consists of moving an
object around a center of rotation. A center of
rotation is a point around which a 2dimensional object is rotated.
The angle of rotation is how much the object
is rotated. When the direction of rotation is important, rotation is referred to as
clockwise
or counterclockwise.

Rotations in 3Dimensions
Click on the blue points and drag them to change the figure.
 Manipulative 2  Rotation about a Line Created with GeoGebra. 

A point is insufficient to define a rotation in a
3dimensional space. While a figure can move
around a point, there is nothing to define the direction of movement. In
3dimensional space, a figure is rotated around a
line.
The line is the center of rotation.

Symmetry of Rotation
Click on the blue points and drag them to change the figure.
Are there any angles of rotation about the center of the circle such that the image is not on top of the preimage?
 Manipulative 3  Rotational Symmetry Created with GeoGebra. 

Symmetry of rotation refers to
geometric figures that, when rotated a certain angle about the center of the object,
are coincidental with the original object. If two objects are coincidental, they are
identical in size, shape, and location. Manipulative 3 shows the symmetry
of rotation of a circle around the center of the circle. For any angle of rotation,
the rotated circle is
coincidental
with the original circle. The rotated circle always looks just like the original circle.

Click on the blue points and drag them to change the figure.
At what angles of rotation does the image lay on top of the preimage?
 Manipulative 4  Rotation of a Square about its Center Created with GeoGebra. 

In manipulative 4, the original square (in blue) and the rotated square are
coincidental only at three angles of rotation:
90° = π / 2 rad,
180° = π rad, and
270° = 3π / 2 rad.

Click on the blue points and drag them to change the figure.
At what angles does the image lie on top of the preimage?
 Manipulative 5  Rotation of a Square about a Corner Created with GeoGebra. 

In manipulative 5, a square is rotated about one of its corners. Notice that the
original square and the rotated square are coincidental only with a full circle
rotation. So the square does not have rotational symmetry about one
of its corners.

References
 McAdams, David E.. All Math Words Dictionary, rotation. 2nd Classroom edition 201501084799968. pg 158. Life is a Story Problem LLC. January 8, 2015. Buy the book
More Information
 McAdams, David E.. Angle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/a/angle.html.
Cite this article as:
McAdams, David E. Rotation. 5/2/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/rotation.html.
Image Credits
Revision History
5/2/2019: Changed equations and expressions to new format. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
12/5/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra app. (
McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (
McAdams, David E.)
3/11/2009: Clarified a center of rotation applying to 2dimensional objects. Rewrote definition of symmetry of rotation to be more mathematically correct (
McAdams, David E.)
11/2/2008: Changed manipulatives to GeoGebra. (
McAdams, David E.)
3/12/2008: Changed see also to match current standard. (
McAdams, David E.)
2/3/2008: Corrected missing manipulative. (
McAdams, David E.)
8/18/2007: Initial version. (
McAdams, David E.)