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Dilations and Scale Factor
Dilations on and off the Coordinate Plane
In this lesson, you will dilate figures on and off 
the coordinate plane. You will use scale factors
greater than 1 to make enlargements, and 
scale factors less than 1 to make reductions. 
You will use centers of dilation of the origin
as well as other centers of dilation.
2
-2
4
-4
6
-6
2
-2
4
-4
6
-6
8
-8
10
-10
Use a scale factor of 3
to dilate trapezoid KLMNover the origin.
K
L
L (0, 2)
M
N
L' (      ,      )
2
-2
4
-4
6
-6
2
-2
4
-4
6
-6
8
-8
10
-10
Use a scale factor of 3
to dilate trapezoid KLMNover the origin.
K
L
K (-2, -1) → K' (       ,       )
M
N
2
-2
4
-4
6
-6
2
-2
4
-4
6
-6
8
-8
10
-10
Use a scale factor of 3
to dilate trapezoid KLMNover the origin.
K
L
N (3, -1) → N' (       ,      )
M
N
2
-2
4
-4
6
-6
2
-2
4
-4
6
-6
8
-8
10
-10
Use a scale factor of 3
to dilate trapezoid KLMNover the origin.
K
L
M (3, 2)  →  M' (       ,       )
M
N
3
B
A
To find the scale factor of a dilation, write a ratio of:  the image to the original.Write the ratio in simplest form.
How to determine the Scale Factor!
4
5
C
B'
6
A'
Scale Factor: 
8
10
C'
3 in
D
F
E
9 in
D'
F'
Find the scale factor:
(reduce)
ORIGINAL
IMAGE
E'
=
2
-2
4
-4
6
-6
2
-2
4
-4
6
-6
8
-8
10
-10
ORIGINAL
Find the scale factor:
(reduce)
IMAGE
=
V
T
T'
V'
R'
S'
R
S
How to dilate a figure on the coordinate plane using a point other than the origin as the center of dilation:
(2,1)
P (4, 2)
Dilate Point P using a scale factor of 2, over a center of
dilation with coordinates (2, 1).
(2,1)
P (4, 2)
Whereas, a scale factor 
of "1/2" means point P' 
will be   ?      the distance to the center of dilation as point P is.
A scale factor of "2" means point P' will be     ?      the distance to the center of dilation as point P is.
twice
?
half
?
7
8
6
3
5
4
2
1
        1     2     3     4     5     6     7    8
Dilate Point P using a scale factor of 2, over a center of
dilation with coordinates (2, 1).
(2,1)
P (4, 2)
Determine the 
coordinates of 
image point P':
(6, 3)
(3, 1.5)
(7, 3)
(8, 4)
Dilate Point P using a scale factor of 1/2, over a center ofdilation with coordinates (4, 0).
P (4, 6)
(4,0)
Determine the 
coordinates of 
image point P':
(3, 2)
(2, 3)
(4, 12)
(4, 3)
8
7
6
5
4
3
2
1
0   1    2   3   4    5   6   7   8
(1,1)
over a center of dilation with coordinates (1, 1).
Dilate Point P using a scale factor of 3, 
P (3, 2)
Determine the 
coordinates of 
image point P':
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