8-6 Dilations

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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