What am I learning today? What will I do to show that I learned it? Dilations 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. Course 2

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

EXPANDS Dilations Scale Factor NO CHANGE 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 NO CHANGE

How is scale factor determined? Course 2 Dilations QUESTION How is scale factor determined?

The ratio of the MODEL’s dimensions to the ACTUAL object’s dimensions Course 2 Dilations The ratio of the MODEL’s dimensions to the ACTUAL object’s dimensions Model or dilation Actual or original

Example 1: Finding a Scale Factor Course 2 5-9 Scale Drawings and Scale Models Example 1: Finding a Scale Factor Identify the scale factor. Room Blueprint Length (in.) 144 18 Width (in.) 108 13.5 blueprint length room length 18 144 Write a ratio using one of the dimensions. = 1 8 = Simplify. 1 8 The scale factor is .

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

______ x _________ = ______ Course 2 Dilations Equation: original scale factor dilation ______ x _________ = ______

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

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

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

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

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

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

Check It Out Dilate the figure by a scale factor of 2. What are the vertices of the image? 10 8 6 C 4 2 A B 2 4 6 8 10

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

Check It Out: Continued 10 B’ C’ A’ 8 6 C 4 2 A B 2 4 6 8 10

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. Yes. All the coordinates have been multiplied by a scale factor of 2. 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) A’(1.5,-1.5) B’(7.5,-1.5) C’(1.5,-7.5) D’(7.5,-7.5) 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)

Student Summary Spotlight

The scale factor for Hot Course 2 Dilations Insert Lesson Title Here VOCABULARY K I M 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.