8-6 Dilations
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
8-6 Dilations
Warm Up
Solve.
1.
2.
x = 12
x = 2.5
8-6 Dilations
Problem of the Day
Missy ate one-fourth of a fruit salad and
Kim ate one-eighth of the fruit salad.
What fraction of the fruit salad remains?
8-6 Dilations
Sunshine State Standards
MA.7.G.4.2 Predict the results of
transformations and draw transformed
figures, with and without the coordinate
plane.
8-6 Dilations
A dilation is a transformation that changes
the size, but not the shape, of a figure. After
a dilation, the image of a figure is similar to
the preimage.
8-6 Dilations
Additional Example 1A: Identifying Dilations
Tell whether each transformation is a dilation.
The figures are not similar,
so the transformation
is not a dilation.
8-6 Dilations
Additional Example 1B: Identifying Dilations
Tell whether each transformation is a dilation.
The figures are similar, so the transformation
Is a dilation.
8-6 Dilations
Check It Out: Example 1A
Tell whether each transformation is a dilation.
A
B
6 cm
D
10 cm
C
A’
D’
5 cm
B’
3 cm
C’
The figures are similar, so the transformation
is a dilation.
8-6 Dilations
Check It Out: Example 1B
Tell whether each transformation is a dilation.
X’
Y
13 yd
X
12 yd
5 yd
z
6 yd
6 yd
z’
6 yd
Y’
The figures are not similar, so the transformation
is not a dilation.
8-6 Dilations
Remember!
Similar figures have the same shape but
not necessarily the same size.
8-6 Dilations
Additional Example 2: Using Dilation to Enlarge a
Figure
Draw the vertices of the image of ∆ABC after a
dilation by a scale factor of 2. What are the vertices
of the image?
Write the
coordinates of the
vertices of ABC.
Then multiply the
coordinates by 2 to
find the
coordinates of the
vertices of A'B'C'.
8-6 Dilations
Additional Example 2 Continued
A’B’C’
ABC
A(0, 0)
A’(0  2, 0  2)
A’(0, 0)
B(1, 2)
B’(1  2, 2  2)
B’(2, 4)
C(3, 1)
C’(3  2, 1  2)
C’(6, 2)
The vertices of the image are A’(0, 0), B’(2, 4),
and C’(6, 2).
8-6 Dilations
Additional Example 2 Continued
8-6 Dilations
Check It Out: Example 2A
Find the vertices of the image of each figure
after a dilation by the given scale factor. Then
draw the image.
Scale factor 3
R' (0, 12), S' (12, 6), T' (6, 3)
8-6 Dilations
Check It Out: Example 2B
Find the vertices of the image of each figure
after a dilation by the given scale factor. Then
draw the image.
Scale factor 2
A' (4, 10), B' (10, 10),C' (10, 4), D' (4, 4)
8-6 Dilations
Additional Example 3: Using a Dilation to Reduce a
Figure
Draw the image of ∆DEF after a dilation by a
scale factor of 1 . Then draw the image.
3
Write the coordinates of the vertices of DEF. The
multiply the coordinates by 1/3 to find the coordinates
of the vertices of D‘E‘F'.
DEF
D(3, 3)
D’E’F’
D’(3  1 , 3  1 )
D’(1, 1)
3
3
E(6, 6)
E’(6  1 , 6  1 )
E’(2, 2)
3
3
F(9, 3)
F’(9  1 , 3  1 )
F’(3, 1)
3
3
The vertices of the image are D’(1, 1), E’(2, 2), and
F’(3, 1).
8-6 Dilations
Check It Out: Example 3A
Find the vertices of the image of each figure
after a dilation by the given scale factor. Then
draw the image.
Scale factor 1
3
A' (1, 2), B' (1, 4),C' (3, 4),D' (3, 2)
8-6 Dilations
Check It Out: Example 3B
Find the vertices of the image of each figure
after a dilation by the given scale factor. Then
draw the image.
Scale factor 1
4
D' (1, 2), E' (2, 3), F' (3, 2)
8-6 Dilations
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
8-6 Dilations
Lesson Quiz
Tell whether the transformation is a dilation.
1.
yes
2. Find the vertices of the image
of ∆ABC after a dilation of a scale
factor of 2. Then draw the image.
A'(2, 4), B'(4, 6), C'(8, 0)
8-6 Dilations
Lesson Quiz for Student Response Systems
1. Tell whether the transformation is a dilation.
A. dilation
B. not a dilation
8-6 Dilations
Lesson Quiz for Student Response Systems
2. Tell whether the transformation is a dilation.
A. dilation
B. not a dilation