This document discusses the geometric transformation of dilation. Dilation changes the size of a shape but not its shape. Dilation is specified by a scale factor, where a scale factor greater than 1 enlarges the shape and less than 1 reduces the shape. Examples are given of dilating shapes at scale factors of 75%, 150%, and 100%. Real-world examples of dilation include enlarging photographs and reducing maps on a photocopier. The key aspects of dilation are explained, including that it changes the size but not the shape using a scale factor to specify the amount of enlargement or reduction.

1. TRANSFORMATIONS-II
DILATIONS
Math 103
GEOMETRY
Dr. Farhana Shaheen

2. OBJECTIVES: TRANSFORMATION
 Demonstrate understanding of:
 1. Translations
 2. Rotations
 3. Reflections
 4. Dilations
 Relate symmetry to appropriate transformations.
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3. In geometry, a transformation is a
way to change the position of a
figure.
Transformation
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Types of Transformations
Translations, Rotations, Reflections, and
Dilations

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9. Question for you-
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10. Translation, Rotation, and Reflection all
change the position of a shape, while the
size remains the same.
The fourth transformation that we are
going to discuss is called dilation.
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DILATION
In dilations, the size of the
figure changes.

12. Dilation changes the size of the shape
without changing the shape.
DILATION
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13. DILATION
200%50%
Notice each time the shape transforms the shape
stays the same and only the size changes.
ENLARGEREDUCE
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14. Look at the pictures below
DILATION
Dilate the image with a scale factor
of 75%
Dilate the image with a scale factor
of 150%
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15. Look at the pictures below
DILATION
Dilate the image with a scale factor
of 100%
Why is a dilation of 75% smaller, a
dilation of 150% bigger, and a dilation of
100% the same?
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When you go to the eye doctor, they
dilate you eyes. Let’s try it by turning
off the lights.
DILATION in Real Life

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When you enlarge a photograph or use a
photocopy machine to reduce a map, you
are making dilations.
DILATION in Real Life

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19. Enlarge means to make a shape bigger.
DILATION
Reduce means to make a shape smaller.
The scale factor tells you how much
something is enlarged or reduced.
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DILATION (Scale factor: k =a)
(x, y)  (ax, ay)

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27. DILATION
Find the Scale factor: k =a)
(x, y)  (ax, ay)
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29. Lets try to make sense of all of this
TRANSFORMATIONS
CHANGE THE
POSTION OF A
SHAPE
CHANGE THE SIZE
OF A SHAPE
TRANSLATI
ON
ROTATION
REFLECTIO
N
Change in
location
Turn around
a point
Flip over a
line
DILATION
Change size
of a shape
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30. See if you can identify the transformation that
created the new shapes
TRANSLATION
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31. See if you can identify the transformation that
created the new shapes
REFLECTIONWhere is the line
of reflection?
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32. See if you can identify the transformation that
created the new shapes
DILATION
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33. See if you can identify the transformation that
created the new shapes
ROTATION
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34. See if you can identify the transformation in these
pictures?
REFLECTION
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36. See if you can identify the transformation in these
pictures?
ROTATION
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37. See if you can identify the transformation in these
pictures?
TRANSLATION
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38. See if you can identify the transformation in these
pictures?
DILATION
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39. See if you can identify the transformation in these
pictures?
REFLECTION
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See if you can identify the
transformation in these pictures?

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(Anti-clockwise)