Dilations in the
Coordinate Plane
EQ: How do you describe the properties of
dilation?
How can you describe the effect of dilation
on coordinates using algebraic
Dilations
Dilation
A transformation that changes the size of a
figure. The original figure and transformed
figure are similar.
Corresponding angles are same
Corresponding side lengths are not same; but
proportional
 Center of dilation - The point of projection
In the coordinate plane, the center of
dilation is the origin.

Two types of dilations
Enlargement
Reduction
 The
dilation is an
enlargement if the
scale factor is > 1.
 The
dilation is a
reduction if the scale
factor is between 0
and 1.
Dilations
Scale factor - The amount
of change written as a
ratio
To find the new
coordinates, multiply the
original coordinates by the
scale factor.

Steps to Follow
1.
2.
3.
4.
Plot the given points.
Multiply each coordinate
by the scale factor.
Plot the image points.
State the coordinates of
the dilation.
Finding a Scale Factor
 The
blue triangle is a dilation image of the
red triangle. Describe the dilation.

The center is X. The image is larger than the preimage,
so the dilation is an enlargement.
X 'T ' 4  8

3
XT
4
Finding a Scale Factor
 The
blue quadrilateral is a dilation image
of the red quadrilateral. Describe the
dilation.
Graphing Dilation Images

∆PZG has vertices P(2,0), Z(-1, ½), and G (1, 2).
What are the coordinates of the image of P for
a dilation with center (0,0) and scale factor 3?
a) (5, 3) b) (6,0) c) (2/3, 0) d) (3, -6)
Algebraic Notation of Dilation

In a coordinate plane, dilations whose
centers are the origin have the property
that the pre-image P to image P’ where ‘k’
is the scale factor.
P (x, y)
P’ (kx, ky)
4) Algebraic to verbal
(2, 3)
a) (X, Y)  (2X, 2Y) __________________
b) New coordinates: (
)
b) (X, Y)  (1/4X, 1/4Y)__________________
New coordinates: (
)
c) (X, Y)  (2.5X, 2.5Y)_____________________
New coordinates: (
)
d) (X, Y)  (-2Y, 2X)_______________________
New coordinates: (
)
Given the vertices of the triangle, find a
dilation by a scale factor of 3.
y



A (1,2) A’ (3,6)
B (3,3) B’ (9,9)
C (1,3) C’ (3,9)
C
’
A’
C B
A
B’
x
Given the vertices of the rectangle, find
a dilation by a scale factor of 2/3.
y




A (-6,-3) A’ (-4,-2)
B (-6,3) B’ (-4,2)
C (6,3) C’ (4,2)
B
D (6,-3) D’ (4,-2)
B’
C’
C
x
A
A’
D’
D
DILATION
Triangle:
A (-2, -4)
B (3, -2)
C (1, 2)
D (-4,0)
Color Red
Scale factor of
2
Algebraic
Representation
(x, y)  (
New Coordinates:
A’ (
B’ (
C’ (
D’ (
Color Blue
Scale factor
of 1/2
) (x, y)  (
)
)
)
)
A’’ (
B’’ (
C’’ (
D”(
Color Green
Scale factor
of 3
) (x, y)  (
)
)
)
)
A’’’ (
B’’’ (
C’’’ (
D’’’ (
Color Pink
)
)
)
)
)