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Dilations.  Dilation  Scale Factor  Center of Dilation.

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Presentation on theme: "Dilations.  Dilation  Scale Factor  Center of Dilation."— Presentation transcript:

1 Dilations

2  Dilation  Scale Factor  Center of Dilation

3  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.

4  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.

5  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’?

6  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?

7  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.

8  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 ( ).

9  Page 364 #2-14 even and Workbook page 58


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