Transcript Enlargements

Dilations
Objectives:
To be able to dilate shapes given a scale
factor and centers of dilation.
Find centers of dilation.
Scale factors
and
Centers of Dilation
The size of a dilation is described by its scale factor.
For example, a scale factor of 2 means that the new
shape is twice the size of the original.
The position of the image depends on the location
of the center of dilation.
Dilate triangle A with a
scale factor of 3 and center
of dilation (2,1).
y
10
9
8
7
6
5
4
3
2
1
Draw lines from the center
of the dilation to each
vertex of your shape.
How do I dilate a shape?
A’
Calculate the distance from
the center of the dilation to
a vertex of the preimage
and multiply it by the scale
factor to find the distance
the image point is from the
center.
Repeat for all the
other vertices.
A
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Connect your new
points to create your
dilated shape.
x
What if the center of dilation
is inside the shape?
y
9
8
7
6
5
4
3
2
1
Dilate shape B
with scale factor 2
and with a center
of dilation (6,6).
B
B’
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x
What about scale
factors less than 1?
y
9
8
7
6
5
4
3
2
1
Dilate the quadrilateral
by scale factor ½ and
center of dilation (10,1).
Each vertex on the
dilated shape is half
the distance from the
center than its
corresponding vertex
on the original shape.
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Even though the
shape gets smaller,
it’s still called a
x dilation.
How do I find the center of
dilation?
y
10
9
8
7
6
5
4
3
2
1
Connect the corresponding
vertices and extend the lines.
The point where they all
intersect is your center of
dilation.
E
Center = (2,9)
D
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What was the scale
factor of the
dilation?
x