Dilations
The last transformation we are going to look at is dilations.
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Dilation simply makes an image bigger or smaller. It does not change the shape of the object, but enlarges it or reduces it. The amount that the object is enlarged or reduced is called the scale factor. |
Take a look at the following dilations.
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Dilation |
Notice that the dark yellow star has been reduced to make the lighter yellow star. The result is a star that is the same shape, but is smaller. This dilation has a scale factor that has an absolute value less than 1.
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Dilation |
Notice that the dark blue moon has been enlarged to make the lighter blue moon. The result is a moon that is the same shape, but is larger. This dilation has a scale factor that has an absolute value greater than 1.
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Dilation |
Notice again, that the dilation shown above is an enlargement. As we stated earlier, the scale factor of a dilation that is an enlargement is greater than 1. Each dimension of the new image is the corresponding dimension of the original image times the scale factor.
Let’s find the scale factor of this dilation.
L’ = L·f, where f is the scale factor.
12 = 8·f
= f
W’ = W·f
6 = 4·f
= f
The scale factor for this dilation is
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