Post on 15-Mar-2020
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Transformation
--A change in position, shape, or size of a figure.
Chapter 3
Transformations: Shapes in Motion
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Preimage
-- the original figure
Image
-- the transformed figure
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Isometry
-- a transformation in which the original figure and its image are congruent
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Translation
-- a transformation that moves points the same distance and in the same direction
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* A translation slides a figure from one position to another.
* A translation is an isometry.A
B C
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http://www.mathsisfun.com/geometry/translation.html
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HW # 32: Translations 1
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Ordered pair notation can be used to describe a translation.
Example:
Translate ( 2 , 3 )
means that each point is translated 2 units to the right (in the xdirection or horizontally) and 3 units down (in the y direction or vertically)
** This is also called vector notation.
** You can find the image by
adding 2 to each xcoordinate
& subtracting 3 from each
ycoordinate.
J (6, 2) J'
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Example:
What is the image of each point under the translation ( 1, 4 ) ?
A (3, 3) A' =
B (2, 2) B' =
C (3, 5) C' =
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What vector describes the translation
G H ?
G (4, 3) H (0, 1)
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Composition a combination of any two transformations in which the second transformation is performed on the image of the first transformation.
** A composition of translations can be rewritten as a single translation.
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Example:
Find a single translation that has the same effect as each compositon of translations.
1. (9, 4) followed by (7, - 2)
2. (-12, 6) followed by (12, 4)
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HW # 33
p. 135 - 136 # 1-12, 18, 21, 24 - 26