﻿ Dilation: A geometric transformation that produces a similar shape by changing the size and location of the original shape.

# Dilation

Pronunciation: /dɪˈleɪ ʃən/ ?

 Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) Manipulative 1: Dilation. Created with GeoGebra.

 Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) 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. dilation. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=dilation&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
2. Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen. Geometry, pp 592-598. Houghton Mifflin McDougal Littell, January 2000.
3. Lawrence S. Leff. E-Z Geometry, 4th Edition, pg 434. Barron's Educational Series, April 1, 2009.

• McAdams, David. Scale. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2010-02-18. http://www.allmathwords.org/article.aspx?lang=en&id=Scale.

### Educator Resources

• Scale Modeling. NASA Connect. NASA LaRC Office of Education. 2010-02-18. http://www.archive.org/details/NasaConnect-Vt-scaleModeling.
• Model Testing. NASA Connect. NASA LaRC Office of Education. 2010-02-18. http://www.archive.org/details/NasaConnect-Xpg-ModelTesting.

### Printed Resources

Dilation. 2011-06-02. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/dilation.html.

### Revision History

2011-06-02: Added definition of enlargement (McAdams, David.)