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Pre-Algebra
7-5 Dilations7-5 Dilations
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Pre-Algebra
7-5 Dilations
Warm UpMultiply.
1. 4 2. 12
3. 24 4. –36
Pre-Algebra
7-5 Dilations
3
18
10
9
–27
30
3 4
3 4
3 4
3 4
5. 4 2.5 6. 12 2.5
Pre-Algebra
7-5 Dilations
Problem of the Day
Every day, a plant grows to three times its size. Every night, it shrinks to half its size. After three days and nights, it is 6.75 in. tall. How tall was the plant at the start?
2 in.
Pre-Algebra
7-5 Dilations
Learn to identify and create dilations of plane figures.
Pre-Algebra
7-5 Dilations
Vocabulary
dilationscale factorcenter of dilation
Pre-Algebra
7-5 Dilations
Your pupils are the black areas in the center of your eyes. When you go to the eye doctor, the doctor may dilate your pupils, which makes them larger.
Pre-Algebra
7-5 Dilations
Translations, reflections, and rotations are transformations that do not change the size or shape of a figure. A dilation is a transformation that changes the size, but not the shape, of a figure. A dilation can enlarge or reduce a figure.
Pre-Algebra
7-5 Dilations
A scale factor describes how much a figure is enlarged or reduced. A scale factor can be expressed as a decimal, fraction, or percent. A 10% increase is a scale factor of 1.1, and a 10% decrease is a scale factor of 0.9.
Pre-Algebra
7-5 Dilations
A scale factor between 0 and 1 reduces a figure. A scale factor greater than 1 enlarges it.
Helpful Hint
Pre-Algebra
7-5 Dilations
Tell whether each transformation is a dilation.
The transformation is a dilation.
The transformation is not a dilation. The figure is distorted.
Additional Example 1A & 1B: Identifying Dilations
A. B.
Pre-Algebra
7-5 Dilations
Tell whether each transformation is a dilation.
The transformation is a dilation.
The transformation is not a dilation. The figure is distorted.
Additional Example 1C & 1D: Identifying Dilations
C. D.
Pre-Algebra
7-5 Dilations
Tell whether each transformation is a dilation.
A'
B' C'
A
B C
A.
B
A
C
A'
B' C'
The transformation is a dilation.
The transformation is not a dilation. The figure is distorted.
Try This: Example 1A & 1B
B.
Pre-Algebra
7-5 Dilations
Tell whether each transformation is a dilation.
C.
The transformation is a dilation.
The transformation is not a dilation. The figure is distorted.
Try This: Example 1C & 1D
A'
B' C'
A
B C
D.
A'
B' C'
A
B C
Pre-Algebra
7-5 Dilations
Every dilation has a fixed point that is the center of dilation. To find the center of dilation, draw a line that connects each pair of corresponding vertices. The lines intersect at one point. This point is the center of dilation.
Pre-Algebra
7-5 Dilations
Dilate the figure by a scale factor of 1.5 with P as the center of dilation.
Additional Example 2: Dilating a Figure
Multiply each side by 1.5.
Pre-Algebra
7-5 Dilations
Dilate the figure by a scale factor of 0.5 with G as the center of dilation.
G
F H
2 cm 2 cm
2 cm
Multiply each side by 0.5.
Try This: Example 2
G
F H
2 cm 2 cm
2 cm
F’ H’1 cm
1 cm
1 cm
Pre-Algebra
7-5 DilationsAdditional Example 3A: Using the Origin as the Center of
DilationDilate the figure in Example 3A on page 363 by a scale factor of 2. What are the vertices of the image?
Multiply the coordinates by 2 to find the vertices of the image.
A(4, 8) A’(4 2, 8 2) A’(8, 16)
B(3, 2) B’(3 2, 2 2) B’(6, 4)
C(5, 2) C’(5 2, 2 2) C’(10, 4)
The vertices of the image are A’(8, 16), B’(6, 4), and C’(10, 4).
ABC A’B’C’
Pre-Algebra
7-5 Dilations
Additional Example 3B: Using the Origin as the Center of Dilation
Dilate the figure in Example 3B by a scale factor
of . What are the vertices of the image?1 3
The vertices of the image are A’(1, 3), B’(3, 2), and C’(2, 1).
ABC A’B’C’
A(3, 9) A’(3 , 9 ) A’(1, 3) 1 3
1 3
B(9, 6) B’(9 , 6 ) B’(3, 2) 1 3
1 3
C(6, 3) C’(6 , 3 ) C’(2, 1) 1 3
1 3
Multiply the coordinates by to find the vertices of the image.
1 3
Pre-Algebra
7-5 Dilations
Try This: Example 3A
Dilate the figure by a scale factor of 2. What are the vertices of the image?
2
4
2 4 6 8 100
6
8
10
B
C
A
Pre-Algebra
7-5 Dilations
Try This: Example 3A Continued
A(2, 2) A’(2 2, 2 2) A’(4, 4)
B(4, 2) B’(4 2, 2 2) B’(8, 4)
C(2, 4) C’(2 2, 4 2) C’(4, 8)
ABC A’B’C’
The vertices of the image are A’(4, 4), B’(8, 4), and C’(4, 8).
Pre-Algebra
7-5 Dilations
Try This: Example 3A Continued
2
4
2 4 6 8 100
6
8
10
B’
C’
A’
B
C
A
Pre-Algebra
7-5 Dilations
Try This: Example 3B
Dilate the figure by a scale factor of 0.5. What are the vertices of the image?
2
4
2 4 6 8 100
6
8
10
B
C
A
Pre-Algebra
7-5 Dilations
Try This: Example 3B Continued
A(4, 5) A’(4 0.5, 5 0.5) A’(2, 2.5)
B(8, 5) B’(8 0.5, 5 0.5) B’(4, 2.5)
C(4, 9) C’(4 0.5, 9 0.5) C’(2, 4.5)
ABC A’B’C’
The vertices of the image are A’(2, 2.5), B’(4, 2.5), and C’(2, 4.5).
Pre-Algebra
7-5 Dilations
Try This: Example 3B Continued
2
4
2 4 6 8 100
6
8
10
B
C
A
B’
C’
A’
Pre-Algebra
7-5 Dilations
Lesson Quiz
1. Tell whether the transformation is a dilation. A(0, 4) B(5,5) C(3,3) A’(0, 8) B’(10, 10) C’(6, 6)
2 4 6
-2
-4
-6
P
AB
C
2. Dilate the figure by a scale factor of 1.5 with P as the center of dilation.
3. Dilate the figure by a scale factor of 2 with the origin as the center of dilation. What are the coordinates of the image? A(2,4) B(5,6) C(6,1)