The document defines key concepts about vectors and translations: - A translation slides every point of a figure the same distance and direction, preserving angles and lengths, making it an isometry. - A vector has both direction and magnitude, with an initial and terminal point. It can be represented by its horizontal and vertical components. - A translation theorem states that a translation is an isometry because it preserves the congruence of figures.

1. 9.1 Vectors January 23, 2013
9.1 Translation using Vectors
Image: new figure
Preimage: original figure
Translation: slides every point the same distance
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2. 9.1 Vectors January 23, 2013
Isometry: transformation that preserves length & angle
measure
(congruence transformation)
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3. 9.1 Vectors January 23, 2013
Translation Theorem: A translation is an isometry.
B'
B
ABC ≅ A'B'C'
A' C'
A C
Vector: a quantity that has both direction and magnitude (size)
Vector FG: FG Terminal (ending)
Point: G
G
Initial (starting)
Point: F vertical component
F
horizontal component
Component Form: horizontal & vertical components 5,2
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4. 9.1 Vectors January 23, 2013
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5. 9.1 Vectors January 23, 2013
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6. 9.1 Vectors January 23, 2013
HW pg. 576 #4­28 evens
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