Difference between revisions of "Dilation"
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Conversely, any two similar figures in a plane are dilations of each other. These figures are called [[homothetic]] figures. These figures are special, because if we drew lines through corresponding parts of the two figures, they would intersect at a common point <math>O</math>, the center of dilation. | Conversely, any two similar figures in a plane are dilations of each other. These figures are called [[homothetic]] figures. These figures are special, because if we drew lines through corresponding parts of the two figures, they would intersect at a common point <math>O</math>, the center of dilation. | ||
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Revision as of 00:18, 21 May 2013
A dilation is, simply put, and enlargement or shrinking of an object. This is also known as a similitude, which means that the figure is getting bigger or smaller by some factor. A dilation is performed as follows:
Suppose we have a plane figure. Without loss of generality, say it is a quadrilateral, 
.
Now, choose a center of dilation, and name it 
. Choose an arbitrary factor of dilation 
Draw 
. Multiply the length by to get 
. Do this for all points to get quadrilateral 
.
In general, we say that the planar figure with vertices 
dilated by a factor around a center results in the vertices 
such that 
= , 
= 
, etc.
The resulting figures are similar (with congruence iff the factor is 1), and are oriented the same way, meaning any distances between the points are of the same ratio. For example, 
. The areas are in a ratio of 
.
Conversely, any two similar figures in a plane are dilations of each other. These figures are called homothetic figures. These figures are special, because if we drew lines through corresponding parts of the two figures, they would intersect at a common point , the center of dilation.
