Section 12-7 Dilations SPI 32D: determine whether the plane figure has been dilated given a diagram and vice versa

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Section 12-7 Dilations SPI 32D: determine whether the plane figure has been dilated given a diagram and vice versa. Objectives: Locate dilation images of figures. Vocabulary. Scale Factor describes the size change from original figure to image Dilation
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Section 12-7 DilationsSPI 32D: determine whether the plane figure has been dilated given a diagram and vice versa
  • Objectives:
  • Locate dilation images of figures
  • Vocabulary
  • Scale Factor
  • describes the size change from original figure to image
  • Dilation
  • transformation whose preimage and image are similar
  • has a center
  • scale factor greater than zero
  • For any point R, R’ is on CR and CR’ = n · CRDilationIn general, a dilation with center C and scale factor n, is a transformation for which the following are true:
  • the image of C is itself (C = C’)
  • n · CRR’RC = C’ (Center)EnlargementsEnlargementsDilation is an enlargement if the scale factor is > 1.B’C’The diagram is an enlargement with a scale factor of 2.imageBC42preimageA’ = A (Center)DD’ReductionsReductionsDilation is a reduction if the scale factor is between 0 and 1.FGF’G’The diagram is a reduction with center C and a scale factor of ¼ .image.CE’H’EHFinding Scale FactorsCircle A with 3-cm diameter and center C is a dilation of concentric circle B with 8-cm diameter. Describe the dilation.The circles are concentric, so the dilation has center C. Because the diameter of the dilation image is smaller, the dilation is a reduction. diameter of dilation imagediameter of preimage38=scale factor:38The dilation is a reduction with center C and scale factor . 1 200The floor plan is a reduction of the actual dimensions by a scale factor of . Real-World and DilationsThe scale factor on a museum’s floor plan is 1 : 200. The length and width on the drawing are 8 in. and 6 in. Find the actual dimensions in feet and inches.Multiply each dimension on the drawing by 200 to find the actual dimensions. Then write the dimensions in feet and inches.8 in. X 200 = 1600 in. = 133 ft, 4 in.6 in. X 200 = 1200 in. = 100 ftThe museum floor measures 133 ft, 4 in. by 100 ft.
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