2. Holt Geometry
12-7 Dilations
Warm Up
1. Translate the triangle with vertices A(2, –1),
B(4, 3), and C(–5, 4) along the vector <2, 2>.
2. ∆ABC ~ ∆JKL. Find the value of JK.
A'(4,1), B'(6, 5),C(–3, 6)
5. Holt Geometry
12-7 Dilations
Recall that a dilation is a transformation that
changes the size of a figure but not the shape.
The image and the preimage of a figure under a
dilation are similar.
6. Holt Geometry
12-7 Dilations
Example 1: Identifying Dilations
Tell whether each transformation appears to
be a dilation. Explain.
A. B.
Yes; the figures are
similar and the image is
not turned or flipped.
No; the figures are not
similar.
7. Holt Geometry
12-7 Dilations
Check It Out! Example 1
a. b.
Yes, the figures are
similar and the image
is not turned or
flipped.
No, the figures are
not similar.
Tell whether each transformation appears to
be a dilation. Explain.
8. Holt Geometry
12-7 Dilations
For a dilation with scale factor k, if k > 0, the
figure is not turned or flipped. If k < 0, the figure
is rotated by 180°.
Helpful Hint
10. Holt Geometry
12-7 Dilations
A dilation enlarges or reduces all dimensions
proportionally. A dilation with a scale factor
greater than 1 is an enlargement, or expansion.
A dilation with a scale factor greater than 0 but
less than 1 is a reduction, or contraction.
11. Holt Geometry
12-7 Dilations
Example 2: Drawing Dilations
Copy the figure and the center of dilation P.
Draw the image of ∆WXYZ under a dilation
with a scale factor of 2.
Step 1 Draw a line through
P and each vertex.
Step 2 On each line,
mark twice the
distance from P to the
vertex.
Step 3 Connect the
vertices of the image.
W’ X’
Z’Y’
12. Holt Geometry
12-7 Dilations
Check It Out! Example 2
Copy the figure and the center of dilation.
Draw the dilation of RSTU using center Q and
a scale factor of 3.
Step 1 Draw a line through
Q and each vertex.
Step 2 On each line,
mark twice the
distance from Q to
the vertex.
Step 3 Connect the
vertices of the image.
R’ S’
T’U’
13. Holt Geometry
12-7 Dilations
Example 3: Drawing Dilations
On a sketch of a flower, 4 in. represent 1 in.
on the actual flower. If the flower has a 3 in.
diameter in the sketch, find the diameter of
the actual flower.
The scale factor in the dilation is 4, so a 1 in. by 1
in. square of the actual flower is represented by a
4 in. by 4 in. square on the sketch.
Let the actual diameter of the flower be d in.
3 = 4d
d = 0.75 in.
14. Holt Geometry
12-7 Dilations
Check It Out! Example 3
What if…? An artist is creating a large painting
from a photograph into square and dilating
each square by a factor of 4. Suppose the
photograph is a square with sides of length 10
in. Find the area of the painting.
The scale factor of the dilation is 4, so a 10 in.
by 10 in. square on the photograph represents a
40 in. by 40 in. square on the painting.
Find the area of the painting.
A = l w = 4(10) 4(10)
= 40 40 = 1600 in2
16. Holt Geometry
12-7 Dilations
If the scale factor of a
dilation is negative, the
preimage is rotated by
180°. For k > 0, a dilation
with a scale factor of –k is
equivalent to the
composition of a dilation
with a scale factor of k that
is rotated 180° about the
center of dilation.
17. Holt Geometry
12-7 Dilations
Example 4: Drawing Dilations in the Coordinate Plane
Draw the image of the triangle with vertices
P(–4, 4), Q(–2, –2), and R(4, 0) under a
dilation with a scale factor of centered at the
origin.
The dilation of (x, y) is
19. Holt Geometry
12-7 Dilations
Check It Out! Example 4
Draw the image of the triangle with vertices
R(0, 0), S(4, 0), T(2, -2), and U(–2, –2) under
a dilation centered at the origin with a scale
factor of .
The dilation of (x, y) is
21. Holt Geometry
12-7 Dilations
Lesson Quiz: Part I
1. Tell whether the transformation appears to be a
dilation.
yes
2. Copy ∆RST and the center of dilation. Draw the
image of ∆RST under a dilation with a scale of .
22. Holt Geometry
12-7 Dilations
3. A rectangle on a transparency has length 6cm and
width 4 cm and with 4 cm. On the transparency 1
cm represents 12 cm on the projection. Find the
perimeter of the rectangle in the projection.
Lesson Quiz: Part II
4. Draw the image of the triangle with vertices
E(2, 1), F(1, 2), and G(–2, 2) under a dilation with
a scale factor of –2 centered at the origin.
240 cm
