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Dilations over the Origin and Scale Factor
Contributed by: Miles
(Original author: Warren)
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
M (3, 2) → M' (       ,      )
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
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 ½
to dilate rectangle EFGHover the origin.
E (0, 0) → E' (      ,      )
E
H
G
F
2
-2
4
-4
6
-6
2
-2
4
-4
6
-6
8
-8
10
-10
Use a scale factor of ½
to dilate rectangle EFGHover the origin.
F (10, 0) → F' (      ,      )
E
H
G
F
2
-2
4
-4
6
-6
2
-2
4
-4
6
-6
8
-8
10
-10
Use a scale factor of ½
to dilate rectangle EFGHover the origin.
G    → G' (     ,      )
E
H
G
F
2
-2
4
-4
6
-6
2
-2
4
-4
6
-6
8
-8
10
-10
Use a scale factor of ½
to dilate rectangle EFGHover the origin.
H  → H' (       ,       )
E
H
G
F
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
=
T
V
V'
T'
R'
S'
R
S
Find the scale factor:
Δ PSU is a dilation of Δ RST.
8
½
16
2
R
8
P
8
S
U
T
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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