Presentation on theme: "What am I learning today? What will I do to show that I learned it?"— Presentation transcript:
1 What am I learning today? What will I do to show that I learned it? DilationsWhat am I learning today?DilationsWhat 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
2 How does the scale factor determine what will happen to the figure? Course 2DilationsQUESTIONHow does the scale factor determine what will happen to the figure?
3 EXPANDS Dilations Scale Factor NO CHANGE Course 2DilationsScale FactorIf your scale factor is greater than 1,the imageIf your scale factor is less than 1, theimageIf your scale factor is 1, there isEXPANDSSHRINKSNOCHANGE
4 How is scale factor determined? Course 2DilationsQUESTIONHow is scale factor determined?
5 The ratio of the MODEL’s dimensions to the ACTUAL object’s dimensions Course 2DilationsThe ratio of the MODEL’s dimensions to the ACTUAL object’s dimensionsModel or dilationActual or original
6 Example 1: Finding a Scale Factor Course 25-9Scale Drawings and Scale ModelsExample 1: Finding a Scale FactorIdentify the scale factor.RoomBlueprintLength (in.)14418Width (in.)10813.5blueprint lengthroom length18144Write a ratio using one of the dimensions.=18=Simplify.18The scale factor is .
7 What is the equation that is used for all dilations? Course 2DilationsQUESTIONWhat is the equation that is used for all dilations?
8 ______ x _________ = ______ Course 2DilationsEquation:originalscale factordilation______ x _________ = ______
9 Dilations d = 8 d = 1 Examples 4 2 d 2 .5 d Course 2DilationsExamples42doriginal x scale factor = dilation4?d = 8SF: 22.5doriginal x scale factor = dilation2?d = 1SF: .5
10 How is the missing value in a dilation found? Course 2DilationsQUESTIONHow is the missing value in a dilation found?
11 Dilations To find the missing value: Use the equation. Substitute the Course 2DilationsTo find the missing value:Use the equation. Substitute thegiven information. Use a variablefor the unknown.2. Solve for the variable.
12 Dilations s = 1.4 s = 5 Examples 4 s 5.6 2 s 10 Course 2DilationsExamples4s5.6original x scale factor = dilation45.6s = 1.4SF: ?2s10original x scale factor = dilation210s = 5SF: ?
13 How do I dilate an object on the coordinate plane? Course 2DilationsQUESTIONHow do I dilate an object on the coordinate plane?
14 Dilations Find the coordinates of the preimage. Course 2DilationsTo 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.
15 Check It OutDilate the figure by a scale factor of 2. What are the vertices of the image?1086C42AB246810
16 Check It Out: Continued A’B’C’ABCA(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).
18 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)
20 The scale factor for Hot Course 2DilationsInsert Lesson Title HereVOCABULARYKIMdilationtransformationcauses figure to increase or decrease proportionatelyEye doctors “dilate” your eyesscalefactorratioenlarges or shrinks similar figuresThe scale factor for HotWheels®cars is 1:64.
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