Dilations: StretchingShrinking

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
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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)

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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?