DILATION

By Alex Tainter and Julia Bradley

What is it?

A dilation is a transformation in which a polygon is enlarged or reduced by a given factor around a given center point.

Scale factor- The ratio of any two corresponding lengths in two similar geometric figures.

On a coordinate plane, each point on the shape given will have an x value and a y value. Each of these values will be multiplied by the scale factor. The end result should be the points of the dilated shape. The function rule is as shown below

FUNCTION RULE

Ds (x,y)=(sx,sy)


s= scale factor

Ds= dilation of scale factor (s)

Example 1

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In this example, the scale factor is 1/2. Since the scale factor of the dilation is less than one, the shape's size is decreased. This is known as reduction.

Example 2

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In this example, the scale factor is 2. Since the scale factor of the dilation is greater than one, the shape's size is increased. This is known as enlargement.

Example 3

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This example shows the dilation with the center point showing, and how the shapes both line up with it. The center point is usually (0,0), but it can also be any other point on the coordinate plane.
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