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Lesson 9-7 Dilations Rigor: Dilate figures on and off a coordinate plane, calculate the scale factor of a dilation Relevance โ Optometry, art, graphic design
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What is a Dilation? A dilation is a transformation that maps
k A dilation is a transformation that maps a pre-image onto an image by multiplying the distance from the center of dilation to each vertex by a scale factor (k). Dilation is an ACTION that produces similar figures. Coordinate notation: (x,y) ๏ (kx, ky) Scale factor = ๐๐๐๐๐ ๐๐๐๐๐กโ ๐๐๐โ๐๐๐๐๐ ๐๐๐๐๐กโ The corresponding segments/ lines are parallel to each other
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Enlargements and Reductions
Reduction: -1 < scale factor < 1 The center of dilation can be inside, outside, or on the figure. The center of dilation determines the position of the image, the scale factor determines the size.
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EX 1: What is the scale factor
EX 1: What is the scale factor? Is the dilation a reduction or an enlargement? The image is in blue, and the pre-image is in black. A) B)
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k = 2 B) y = x + 4; (x, y) ๏ (1/2x, 1/2y)
EX 2: Graph the image after a dilation about the origin with the given scale factor. k = B) y = x + 4; (x, y) ๏ (1/2x, 1/2y)
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EX 3: An artist is creating a large painting from a photo by dividing the photo into squares and dilating each square by a scale factor of 4. If the photo is 20cm by 25cm, what is the perimeter of the painting?
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Negative Scale Factors
If k is negative, the transformation is a composition of a dilation & a 180o rotation about the center of dilation EX 4: Draw ฮABC and its image if ฮABC has vertices A(-1,1), B( -3, -1), and C( -1, -2) under the dilation centered at the origin and k = - 2.
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EX 5: Constructions! Turn to workbook page 405 example 1
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9-7 Classwork Textbook pg 653 Problems: #2 โ 12 even, 18, 28, 29
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Honors: 9-7 Assignments Primary Assignment: Due Friday
Website: join.quizizz.com Codes: Period 2: Period 4: Period 6: Secondary Assignment: Workbook pg 407 #1 & 3 Textbook pg 653 #7 โ 19 odd, 27, 30, 32
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Standard: 9-7 Assignments
Primary Assignment: Due Monday Website: join.quizizz.com Codes: Period 1: Period 5: Period 7: Secondary Assignment: Worbook pg 407 #1 & 3 Textbook pg 653 #7 โ 19 odd, 27, 30, 32
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