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Course 2 What am I learning today? Dilations What will I do to show that I learned it? Given a figure in the coordinate plane, determine the coordinates resulting from a dilation. Dilations

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Course 2 Dilations QUESTION How does the scale factor determine what will happen to the figure?

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Course 2 Dilations Scale Factor If your scale factor is greater than 1, the image If your scale factor is less than 1, the image If your scale factor is 1, there is EXPANDS SHRINKS CHANGE NO

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Course 2 Dilations QUESTION How is scale factor determined?

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Course 2 Dilations The ratio of the MODELs dimensions to the ACTUAL objects dimensions Model or dilation Actual or original

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Identify the scale factor. Example 1: Finding a Scale Factor Course Scale Drawings and Scale Models RoomBlueprint Length (in.)14418 Width (in.) blueprint length room length = The scale factor is. Write a ratio using one of the dimensions. Simplify =

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Course 2 Dilations QUESTION What is the equation that is used for all dilations?

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Course 2 Dilations Equation: ______ x _________ = ______ originalscale factordilation

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Course 2 Dilations Examples 2 ? original x scale factor = dilation 2.5d 4 ? original x scale factor = dilation 42 SF: 2 d SF:.5 d = 8 d = 1

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Course 2 Dilations QUESTION How is the missing value in a dilation found?

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Course 2 Dilations 1. Use the equation. Substitute the given information. Use a variable for the unknown. 2. Solve for the variable. To find the missing value:

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Course 2 Dilations Examples 2 10 original x scale factor = dilation 2 s original x scale factor = dilation 4s SF: ? 5.6 SF: ? s = 1.4 s = 5

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Course 2 Dilations QUESTION How do I dilate an object on the coordinate plane?

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Course 2 Dilations 1. Find the coordinates of the preimage. 2.Multiply BOTH x and y by the scale factor. 3.Plot the new image. To perform a dilation on the coordinate plane:

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Course Dilations Check It Out Dilate the figure by a scale factor of 2. What are the vertices of the image? B C A

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Course Dilations Check It Out: 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 The vertices of the image are A(4, 4), B(8, 4), and C(4, 8).

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Course Dilations Check It Out: Continued B C A B C A

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Course Dilations Now Try These… 1. Tell whether the transformation is a true dilation. A(0, 4) B(5,5) C(3,3) A(0, 8) B(10, 10) C(6, 6) Explain. 2. Dilate the figure by a scale factor of 1.5. What are the coordinates of the dilated image? A(1,-1) B(5,-1) C(1,-5) D(5,-5) 3. Dilate the figure by a scale factor of 2. What are the coordinates of the image? A(2,4) B(5,6) C(6,1) A(4,8) B(10,12) C(12,2) Yes. All the coordinates have been multiplied by a scale factor of 2. A(1.5,-1.5) B(7.5,-1.5) C(1.5,-7.5) D(7.5,-7.5)

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Student Summary Spotlight 19

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Insert Lesson Title Here Course 2 Dilations VOCABULARYKIM dilation - transformation - causes figure to increase or decrease proportionately Eye doctors dilate your eyes scale factor - ratio - enlarges or shrinks similar figures The scale factor for Hot Wheels® cars is 1:64.

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