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8-6 Dilations
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
8-6 Dilations
Warm Up
x = 12 x = 2.5
Solve.
1. 2.
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
MA.7.G.4.2 Predict the results of transformations and draw transformed figures, with and without the coordinate plane.
Sunshine State Standards
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
Tell whether each transformation is a dilation.
The figures are not similar, so the transformation is not a dilation.
Additional Example 1A: Identifying Dilations
8-6 Dilations
Tell whether each transformation is a dilation.
The figures are similar, so the transformation Is a dilation.
Additional Example 1B: Identifying Dilations
8-6 Dilations
Tell whether each transformation is a dilation.
The figures are similar, so the transformation is a dilation.
Check It Out: Example 1A
A’
D’ C’
B’A
D C
B
5 cm
3 cm6 cm
10 cm
8-6 Dilations
Tell whether each transformation is a dilation.
The figures are not similar, so the transformation is not a dilation.
Check It Out: Example 1B
13 yd
12 yd
5 yd 6 yd
6 yd
6 yd
X’
z’ Y’X z
Y
8-6 Dilations
Similar figures have the same shape but not necessarily the same size.
Remember!
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(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)
ABC A’B’C’
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 DilationsCheck 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.
R' (0, 12), S' (12, 6), T' (6, 3)
Scale factor 3
8-6 DilationsCheck 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.
A' (4, 10), B' (10, 10),C' (10, 4), D' (4, 4)
Scale factor 2
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 . Then draw the image. 1 3
The vertices of the image are D’(1, 1), E’(2, 2), and F’(3, 1).
DEF D’E’F’
D(3, 3) D’(3 , 3 ) D’(1, 1) 1 3
1 3
E(6, 6) E’(6 , 6 ) E’(2, 2) 1 3
1 3
F(9, 3) F’(9 , 3 ) F’(3, 1) 1 3
1 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'.
8-6 DilationsCheck 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 DilationsCheck 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
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
8-6 DilationsLesson 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
1. Tell whether the transformation is a dilation.
A. dilation
B. not a dilation
Lesson Quiz for Student Response Systems
8-6 Dilations
2. Tell whether the transformation is a dilation.
A. dilation
B. not a dilation
Lesson Quiz for Student Response Systems