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

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

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  1. 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

  2. For any point R, R’ is on CR and CR’ = n · CR Dilation In 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 · CR R’ R C = C’ (Center)

  3. Enlargements Enlargements Dilation is an enlargement if the scale factor is > 1. B’ C’ The diagram is an enlargement with a scale factor of 2. image B C 4 2 preimage A’ = A (Center) D D’

  4. Reductions Reductions Dilation is a reduction if the scale factor is between 0 and 1. F G F’ G’ The diagram is a reduction with center C and a scale factor of ¼ . image .C E’ H’ E H

  5. Finding Scale Factors Circle 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 image diameter of preimage 3 8 = scale factor: 3 8 The dilation is a reduction with center C and scale factor .

  6. 1 200 The floor plan is a reduction of the actual dimensions by a scale factor of . Real-World and Dilations The 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 ft The museum floor measures 133 ft, 4 in. by 100 ft.

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