Name ____________________________________ Class Period ________
Dilating Figures on a Coordinate Graph
Dilations To dilate a figure means to enlarge or reduce the figure. The scale factor determines
how much larger or smaller the figure will become. A scale factor greater than 1 will enlarge
the figure. A scale factor less than 1 will reduce the figure.
Center of Dilation Where the dilated figure is drawn depends not only on the scale factor, but
also on where the center of dilation is located. When the corresponding points of the original
figure and the dilated figure are connected by straight lines, the single point where all the lines
meet is the center of dilation. The center of dilation may be the origin (0,0) or it may be any
other point, such as a vertex of the original figure.
Center of Dilation at the Origin When the center of dilation is the origin, You can just multiply
the coordinates of the vertices of the original figure by the scale factor to find the coordinates
of the vertices of the dilated figure. That is, the coordinate rule for a dilation with the center of
dilation at the origin is: (𝑥, 𝑦) → (𝑘𝑥, 𝑘𝑦) where 𝑘 is the scale factor.
Dilate each figure using the origin as the center of dilation.
1. ΔABC and a scale factor of 2.
2.
▱STUV and a scale factor of
S
2
.
V
T
U
A
B
1
C
A(
) → Aʹ(
)
S(
) → Sʹ(
)
B(
) → Bʹ(
)
T(
) → Tʹ(
)
C(
) → Cʹ(
)
U(
) → Uʹ(
)
V(
) → Vʹ(
)
3. ΔDEF with center at origin and scale factor of 2.
D
D(
) → Dʹ(
)
E(
) → Eʹ(
)
F(
) → Fʹ(
)
F
E
Dilate each figure using the given point as the center of dilation.
Unfortunately, there is no easy coordinate rule for making dilations when the center of dilation
is a point other than the origin. Instead, you have to multiply the distance from the center of
dilation to each vertex by the scale factor.
4. ΔJKL with center at P and
5.
Trapezoid TPZD with center at P
scale factor of 2.
and scale factor of
1
3
.
D
T
J
P
Z
L
K
P
J(
) → Jʹ(
K(
) → Kʹ(
L(
) → Lʹ(
)
T(
) → Tʹ(
)
)
P(
) → Pʹ(
)
)
Z(
) → Zʹ(
)
D(
) → Dʹ(
)