Transformations II- Math for Interior Design
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TRANSFORMATIONS-II DILATIONS Math 103 GEOMETRY Dr. Farhana Shaheen
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Transcript of Transformations II- Math for Interior Design
TRANSFORMATIONS-IIDILATIONS
Math 103GEOMETRY
Dr. Farhana Shaheen
OBJECTIVES: TRANSFORMATION Demonstrate understanding of: 1. Translations 2. Rotations 3. Reflections 4. Dilations Relate symmetry to appropriate
transformations.
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In geometry, a transformation is a way to change the position of a figure.
Transformation 05/03/2023
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Types of TransformationsTranslations, Rotations, Reflections, and
Dilations
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Question for you-05/03/2023
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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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DILATIONIn dilations, the size of the figure changes.
Dilation changes the size of the shape without changing the shape.
DILATION05/03/2023
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DILATION
200%50%
Notice each time the shape transforms the shape stays the same and only the size changes.
ENLARGEREDUCE
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Look at the pictures belowDILATION
Dilate the image with a scale factor of 75%
Dilate the image with a scale factor of 150%
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Look at the pictures belowDILATION
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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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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DILATION Find the Scale factor: k =a) (x, y) (ax, ay)
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Lets try to make sense of all of this
TRANSFORMATIONSCHANGE THE
POSTION OF A SHAPE
CHANGE THE SIZE OF A SHAPE
TRANSLATION ROTATION REFLECTIO
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Change in location
Turn around a
pointFlip over a
line
DILATION
Change size of a shape
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See if you can identify the transformation that created the new shapes
TRANSLATION
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See if you can identify the transformation that created the new shapes
REFLECTIONWhere is the
line of reflection?
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See if you can identify the transformation that created the new shapes
DILATION
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See if you can identify the transformation that created the new shapes
ROTATION
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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?
ROTATION
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See if you can identify the transformation in these pictures?
TRANSLATION
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See if you can identify the transformation in these pictures?
DILATION
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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)
