A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. (The image is similar to the original object). Dilation is a transformation in which each point of an object is moved along a straight line. The straight line is drawn from a fixed point called the center of dilation. The distance the points move depends on the scale factor. The center of dilation is the only invariant point.
Scale factor =
If the scale factor is greater than 1, the image is an enlargement.
If the scale factor is between 0 and 1, the image is a reduction.
The figure shows two similar triangles PQR and P’Q’R’. Triangle P’Q’R’ is a dilation of triangle PQR. We say that
triangle PQR is transformed onto triangle P’Q’R’ by a dilation
with center at O and scale factor
The following diagrams show the triangle ABC dilated with different scale factors. Scroll down the page for more examples and explanations of dilations.
We will first look at enlargements which are dilations with scale factors greater than 1
Enlarge triangle PQR with O as the center of dilation and a scale factor of 2.
Solution:Step 1: Measure OP.
Enlarge triangle ABC with C as the center of dilation and a scale factor of 3.
Solution:Step 1: Measure CA.
Note that in this example, all the points in the triangle have been transformed except point C, which is the only invariant point.
Draw an image of the figure PQRS. O is the center of dilation and the scale factor is 1.5.
Solution:Step 1: Join OP.
If the scale factor of a dilation is between 0 and 1, the image will be smaller than the object. It is then called a reduction.
Enlarge triangle PQR with O as the center of enlargement and scale factor .
Solution:Step 1 : Join O to P.
We will now look at how to create a dilation on a coordinate plane.Dilations
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