Chapter 9.1 Notes: Translate Figures and Use Vectors

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Chapter 9.1 Notes Translate Figures and Use
Vectors

• Goal You will use a vector to translate a
  figure.

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• A transformation moves or changes a figure in
  some way to produce a new figure called an image.
  
• Another name for the original figure is the
  preimage.
• Ex.1 Graph quadrilateral ABCD with vertices
• A(-1, 2), B(-1, 5), C(4, 6), and D(4, 2). Find
  the image of each vertex after the translation
• Then
  graph the image using prime notation.

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• Ex.2 Draw with vertices R(2, 2),
  S(5, 2), and T(3, 5). Find the image of each
  vertex after the translation
  Graph the image using prime
  notation.
• Ex.3 The image of
  is with endpoints P(-3, 4) and
  Q(2, 1). Find the coordinates of the endpoints
  of the preimage.

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• An isometry is a transformation that preserves
  length and angle measure.
• Isometry is another word for congruence
  transformation.
• Theorem 9.1 Translation Theorem
• A translation is an isometry.

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• Ex.4 Write a rule for the translation of
  to
• Then verify that the
  transformation is an isometry.
• Another way to describe a translation is by using
  a vector.
• A vector is a quantity that has both direction
  and magnitude, or size.

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• Ex.5 Name the vector and write its component
  form.
• a.
• b.

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• Ex.6 The vertices of are A(0, 3),
  B(2, 4), and C(1, 0). Translate
  using the vector
• Ex.7 Name the vector and write its component
  form.
• a. b.
• c.

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• Ex.8 The vertices of are L(2, 2),
  M(5, 3), and n(9,1 ). Translate
  using the vector

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• Ex.9 A boat heads out from point A on one island
  toward point D on another. The boat encounters a
  storm at B, 12 miles east and 4 miles north of
  its starting point. The storm pushes the boat off
  course to point C, as shown.

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• Write the component form of AB.
• Write the component form of BC.
• Write the component form of the vector that
  describes the straight line path from the boats
  current position C to its intended destination D.