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EXAMPLE 3

Photo Stickers. You are making your own photo stickers. Your photo is 4 inches by 4 inches. The image on the stickers is 1.1 inches by 1.1 inches. What is the scale factor of the reduction?. EXAMPLE 3. Find a scale factor.

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EXAMPLE 3

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  1. Photo Stickers You are making your own photo stickers. Your photo is 4 inches by 4 inches. The image on the stickers is 1.1 inches by 1.1 inches. What is the scale factor of the reduction? EXAMPLE 3 Find a scale factor

  2. The scale factor is the ratio of a side length of the sticker image to a side length of the original photo, or . In simplest form, the scale factor is . 11 40 1.1 in. 4 in. EXAMPLE 3 Find a scale factor SOLUTION

  3. EXAMPLE 4 Standardized Test Practice SOLUTION Determine if EFGHis a dilation of PQRSby checking whether the same scale factor can be used to obtain E, F, and G from P, Q, and R.

  4. P(3, 0) E(9, 0) Q(1, 1) F(3, 3) R(0, 2) G(0, 6) S(4, 5) H(3 4, 3 5) = H(12, 15) ANSWER (x, y) (kx, ky) The correct answer is C. CHECK:Draw rays from the origin through each point and its image. EXAMPLE 4 Standardized Test Practice k = 3 k = 3 k = 3 Because k is the same in each case, the image is a dilation with a scale factor of 3. So, you can use the scale factor to find the image H of point S.

  5. The scale factor is the ratio of a side length of the sticker image to a side length of the original 1.1 in. photo, or . 5.5 ANSWER In simplest form, the scale factor is . 1 5 for Examples 3 and 4 GUIDED PRACTICE 3. What If? In Example 3, what is the scale factor of the reduction if your photo is 5.5 inches by 5.5 inches? SOLUTION

  6. ANSWER A dilation with respect to the origin and scale factor k can be described as (x, y) (kx ,ky) if (x,y) = (0,0) then (kx, ky) = (k 0, k 0) = (0, 0). for Examples 3 and 4 GUIDED PRACTICE 4. Suppose a figure containing the origin is dilated. Explain why the corresponding point in the image of the figure is also the origin.

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