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Geometry
7.6 Dilation
Dilation:
A dilation is a transformation that
stretches
or
shrinks
a figure to create a similar figure.
It is a type of
similarity transformation
.
In a dilation, a figure is enlarged or reduced with respect to a fixed point called
center of dilation
.
The
scale factor
of a dilation is the ratio of a side length of the image to the corresponding side length of the original figure.
You can describe a dilation with respect to the origin with the notation
(x,y)
®
(kx,ky)
, where k is the scale factor.
If 0 < k < 1, the dilation is a reduction.
If k>1, the dilation is an enlargement.
Directions:
Using graph paper and dilate the following figures using scale factor of 1, 2, 3, 4 and 1/2.
Answer the following questions. Also write at least 10 examples of your own.
Q 1
: Find the coordinates of the vertex B
^{1}
where the scale factor k = 2 as shown in the figure:
(4, 4)
(2, 4)
(2, 2)
Q 2
: Draw a dilation of the polygon with the given vertices: A(0,0), B(0, 3), C(2, 4), D(2, -1) using the scale factor of 13/2. The coordinates of the vertex D of the image is ______.
(-13/2, 13)
(13, 13/2)
(13, -13/2)
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