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Lesson 7.5 Dilations

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Vocabulary Dilation Scale Factor Center of Dilation

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Dilation A dilation is a transformation that changes the size, but not the shape, of a figure. Remember: translations, reflections, and rotations are transformations that do NOT change the size or shape of a figure. The pupils of your eyes, the black center, works like a camera lens, dilating to let more or less light in, which means it gets smaller or larger.

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Scale Factor A scale factor describes how much a figure is enlarged or reduced. A scale factor can be expressed as a decimal, fraction, or percent. A scale factor between 0 and 1 reduces a figure. A scale factor greater than 1 enlarges the figure. Each point in the figure MUST be either enlarged or reduced by the same scale factor or it is not a dilation.

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Example 1 Figure ABC has coordinates of (3,3), (1,1), and (4,1). It is dilated by a scale factor of 2. Does the figure reduce or enlarge? To find the new coordinates, multiply each number in the ordered pairs by the scale factor. What are the coordinates for the new figure, A’B’C’?

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**Example 2 Rectangle WXYZ has the following side measures:**

WX = 4 cm, XY = 10 cm, YZ = 4 cm, and ZW = 10 cm What are the measures of W’X’Y’Z’ if it is dilated by a scale factor of ½ ? Does this reduce or enlarge the figure?

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Center of Dilation Every dilation has a fixed point that is the center of dilation. To find the center of dilation, draw a line that connects each pair of corresponding vertices. The lines intersect at one point. This point is the center of dilation.

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Example 3 Dilate triangle EFG by a scale factor of 1.5 with F as the center of dilation. E (-8, -4), F ( -4, -4), G (-4, -8) When using one of the given points as the center of dilation, that point remains the same, but the other points are multiplied by the scale factor. This means when dilated, E ( ), F (-4, -4), and G ( ). When the origin is used as the center of dilation, each point is multiplied by the scale factor. This means that if the same triangle is dilated by a scale factor of 1.5 as the origin as the center of dilation, the new coordinates would be E( ), F ( ), and G ( ).

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Assignment Page 364 #2-14 even and Workbook page 58

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