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Dilations: (Stretching/Shrinking)

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Dilations: (Stretching/Shrinking) Dilations use a scale factor to reduce or enlarge shapes. Every dilation has a center and a scale factor. Most of the time it is the ... – PowerPoint PPT presentation

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Title: Dilations: (Stretching/Shrinking)


1
Dilations (Stretching/Shrinking)
  • Dilations use a scale factor to reduce or enlarge
    shapes.
  • Every dilation has a center and a scale factor.
    Most of the time it is the origin (0, 0)
  • Scale Factor tells you how many times larger or
    smaller your image will be.
  • The new shape and the image are similar.
    Dilations are also called similarity
    transformations.

2
Finding a Dilation
  • To find a dilation with center C and scale factor
    n, you can use the following two rules.
  • The image C is itself (meaning CC)
  • For any point R, R is on CR and CR nCR.

3
How do we locate dilation images?
  • A dilation is a transformation who preimage and
    image are similar. A dilation is not an
    isometry.
  • Every dilation has a center and a scale factor n,
    n gt0. The scale factor describes the size change
    from the original figure to the image.

4
Example 1
  • Quadrilateral ABCD has vertices A(-2, -1), B(-2,
    1), C(2, 1) and D(1, -1).
  • Find the coordinates of the image for the
    dilation with a scale factor of 2 and center of
    dilation at the origin.

C
B
B
C
A
D
A
D
5
Example 2
  • F(-3, -3), O(3, 3), R(0, -3) Scale factor 1/3

O
O
F
R
F
R
6
Example 3
  • T(-1, 0), H(1, 0), I(2, -2), S(-2, -2) Scale
    factor 4

T
H
H
T
I
S
I
S
7
  • The dilation is an enlargement if the scale
    factor is gt 1.
  • The dilation is a reduction if the scale factor
    is between 0 and 1.

8
Finding a Scale Factor
  • The blue triangle is a dilation image of the red
    triangle. Describe the dilation.
  • The center is X. The image is larger than the
    preimage, so the dilation is an enlargement.

9
Finding a Scale Factor
  • The blue quadrilateral is a dilation image of the
    red quadrilateral. Describe the dilation.

10
Graphing Dilation Images
  • ?PZG has vertices P(2,0), Z(-1, ½), and G (1,
    -2).
  • What are the coordinates of the image of P for a
    dilation with center (0,0) and scale factor 3?
  • a) (5, 3) b) (6,0) c) (2/3, 0) d) (3, -6)

11
Graphing Dilation Images
  • Solution
  • The scale factor is 3, so use the rule
  • (x, y)?(3x, 3y).
  • P(2,0) ?P(32, 30) or P(6, 0).
  • The correct answer is B.
  • What are the coordinates for G and Z?
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