dilations
DESCRIPTION
High School geometry Dilations Transformations, scale factor, Center of Dilation, introduction,TRANSCRIPT
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Dilations and Similarity
Mr. Saucedo - GEOMETRY - Milby High School
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OBJECTIVE:
•To identify and construct dilations.
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• A dilation is a transformation that changes the size of a figure but not its shape.
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• A scale factor describes how much the figure is enlarged or reduced. For a dilation with scale factor k, you can find the image of a point by multiplying each coordinate by
k: (a, b) → (ka, kb) .
0
A B
CD
A’ B’
C’D’
0
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KEY CONCEPT:
• A Dilation stretches or shrinks a figure.
• The Center of Dilation never changes position. It’s a starting point.
• The Scale Factor tells you how much the dilation stretches or shrinks.
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• If the scale factor of a dilation is greater than 1 (k > 1) , it is an enlargement. If the scale factor is less than 1 (k < 1) , it is a reduction.
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IDENTIFY THE DILATION• Tell whether each transformation is a dilation
A. B.
The transformation is a dilation.
The transformation is not a dilation. The figure is distorted.
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DRAWING A DILATION• Draw a dilation
of quadrilateral ABCD, with vertices A(2,1), B(4,1), C(4,-1), and (1,-1). Use a scale factor of k=2.
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DRAW A DILATION• A triangle has
the vertices A(4,-4), B(8,2), and C(8,-4). Draw its dilation with a scale of ½.
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CAN YOU FIND THE SCALE FACTOR?
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FIND THE DILATION FACTOR:From triangle A to B.
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Find the scale factor from the Red square to the pink square:
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One last thing…
Image Pre-Image
NEW OLD
OR
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INDEPENDENT PRACTICE
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HOMEWORK
Workbook, Section 6.7. Pages: 121-123Problems: 2, 4, 6, 8, 9, 10, 11, 12, 13Pre AP: Add problem 14.