Dilation

Pronunciation: /dɪˈleɪ ʃən/ Explain

Click on the blue points and drag them to change the figure.

What dilation ration copies the object on top of itself?
Manipulative 1 - Dilation Created with GeoGebra.

Click on the blue points and drag them to change the figure.

Where would the center of dilation be to make concentric circles?
Manipulative 2 - Dilation of a Circle Created with GeoGebra.

A dilation is a geometric transformation that can change the size of an object and can change the location of an object.[1] Each dilation has a center and a ratio. The word dilatation means the same thing as dilation.

The center of dilation is the point from which the dilation is measured. Click on the center in figure 1 and drag it to see how changing the center changes the transformation.

The dilation ratio tells how much bigger or smaller the transformation will make the object. Click on the blue point on the slider to change the ratio. You can also click on the blue vertices of the triangle to change the shape of the triangle. Double click on each manipulative to open a full screen version.

Notice in figure 1 that all the lines in the transformed triangle are parallel to the lines in the original triangle. This is a property of dilation. The object created by the dilation is also similar to the original object.

A dilation which makes an object smaller is sometimes called a compression or a contraction. A dilation which makes an object smaller has a dilation ratio of less than 1.

A dilation which makes an object larger is called an enlargement. To make an object larger is to enlarge the object.

Click on the blue points in the manipulatives and drag them to change the figure.

In areas other than pure mathematics such as manufacturing and architecture, dilation is called scaling. When using the term scaling or scale, the dilation ratio is called a scaling factor.

References

  1. Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen. Geometry. pp 592-598. Houghton Mifflin McDougal Littell. January 2000. Buy the book
  2. Lawrence S. Leff. E-Z Geometry. 4th Edition. pg 434. Barron's Educational Series. Barron's. April 1, 2009. Buy the book

More Information

  • McAdams, David E.. Scale. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2/18/2010. http://www.allmathwords.org/en/s/scale.html.

Educator Resources

  • Scale Modeling. NASA Connect. 2/18/2010. http://www.archive.org/details/NasaConnect-Vt-scaleModeling/index.htm.
  • Model Testing. NASA Connect. 2/18/2010. http://www.archive.org/details/NasaConnect-Xpg-ModelTesting/index.htm.

Cite this article as:

McAdams, David E. Dilation. 7/4/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/dilation.html.

Image Credits

Revision History

7/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
6/2/2011: Added definition of enlargement. (McAdams, David E.)
1/23/2010: Added "References". (McAdams, David E.)
7/11/2008: Added text on similarity. Changed manipulatives from Sketchpad to Geogebra (McAdams, David E.)
6/7/2008: Corrected link errors. (McAdams, David E.)
5/2/2008: Initial version. (McAdams, David E.)

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