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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