Similarity.notebook
January 10, 2014
Day 3
DILATIONS
Similarity.notebook
A
January 10, 2014
dilation is a non-isometric
transformation in
which the image and preimage are similar figures.
C
A dilation has a center "C"
and a scale factor "k".
There are two types of dilations:
1. Enlargement: the image is larger than
the preimage
J'
J
C
K
M
K'
M'
L
L'
In an enlargement, the scale factor k
is greater than one.
k > 1
Similarity.notebook
January 10, 2014
2. Reduction: the image is smaller than
the preimage.
A
A'
In a reduction, the scale factor
k is between zero and one.
0 < k < 1
The scale factor can be found by using
corresponding side lengths or
by using the distance to the dilation center, C.
The ratio will always be set up:
k = image
preimage
Similarity.notebook
January 10, 2014
Example 1 Find k in this Enlargement.
A'
A
C
4
7
B
B'
Example 2
If this is a reduction, find k.
B
6
4
C
B'
Similarity.notebook
January 10, 2014
Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement.
Similarity.notebook
January 10, 2014
Dilations on Coordinate Plane
find the image of each vertex by multiplying
each coordinate by the scale factor.
P(x,y)
P'(kx,ky)
Example 1
a.)
k = 1/2 A (6,18) --> A' ( ,
b.)
k = 3 A (4,-2) --> A' ( ,
)
)
Example 2
Find the coordinates and graph
A'B'C' with k = 2.
A(2,1) -->
B(2,3) -->
C(5,1) -->
Similarity.notebook
Example 5
Graph the dilation of (3,4) (-2, 3) (-1, 5) with k = 3.
Example 6
Graph the dilation of
(6,2) (4,6) (8,10)
with k = 1/2
January 10, 2014
Similarity.notebook
January 10, 2014