4.4 Transformations with Matrices

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4.4 Transformations with Matrices

• 2. Reflections and Rotations

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2) Reflections

• A reflection, or flip, is a transformation that
  creates symmetry. 
• You can use matrix multiplication to graph
  reflections in the coordinate plane.
• There are four reflection matrices you are
  responsible for knowing.

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2) Reflections

• Reflection in the y-axis Reflection in the
  x-axis

 
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2) Reflections

• Reflection in the line y x Reflection in the
  line y -x

 
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2) Reflections

• Example 1  Given triangle ABC with A (4, 1), B
  ( 2, 5) and C (0, 2), reflect the triangle
  across the y-axis. Then, sketch the image.

A B C
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2) Reflections

• Example 1  Given triangle ABC with A (4, 1), B
  ( 2, 5) and C (0, 2), reflect the triangle
  across the y-axis. Then, sketch the image.

A B C
y-axis reflection matrix
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2) Reflections

• Example 1  Given triangle ABC with A (4, 1), B
  ( 2, 5) and C (0, 2), reflect the triangle
  across the y-axis. Then, sketch the image.

A B C
A B C
y-axis reflection matrix
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2) Reflections
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2) Reflections

• Example 2 Given triangle ABC where A (4, 1), B
  ( 2, 5) and C (0, 2), reflect the triangle
  across the x-axis. Then, sketch the image.

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2) Reflections

• Example 2 Given triangle ABC where A (4, 1), B
  ( 2, 5) and C (0, 2), reflect the triangle
  across the x-axis. Then, sketch the image.

A B C
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2) Reflections

• Example 2 Given triangle ABC where A (4, 1), B
  ( 2, 5) and C (0, 2), reflect the triangle
  across the x-axis. Then, sketch the image.

A B C
x-axis reflection matrix
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2) Reflections

• Example 2 Given triangle ABC where A (4, 1), B
  ( 2, 5) and C (0, 2), reflect the triangle
  across the x-axis. Then, sketch the image.

A B C
A B C
x-axis reflection matrix
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2) Reflections










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2) Rotations

• A rotation is a transformation that turns a
  figure about a fixed point called a center of
  rotation. 
• You can rotate a figure as much as 360o. 
• In this text, all rotations are counterclockwise
  about the origin.

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2) Rotations

• Rotation of 90o Rotation of 360o
• Rotation of 180o Rotation of 270o

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2) Rotations

• Example 1  Given triangle ABC where A (4, 1), B
  ( 2, 5) and C (0, 2), rotate the triangle
  270.  Then, sketch the image. 

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2) Rotations

• Example 1  Given triangle ABC where A (4, 1), B
  ( 2, 5) and C (0, 2), rotate the triangle
  270.  Then, sketch the image. 

A B C
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2) Rotations

• Example 1  Given triangle ABC where A (4, 1), B
  ( 2, 5) and C (0, 2), rotate the triangle
  270.  Then, sketch the image. 

A B C
270o rotation matrtix
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2) Rotations

• Example 1  Given triangle ABC where A (4, 1), B
  ( 2, 5) and C (0, 2), rotate the triangle
  270.  Then, sketch the image. 

A B C
A B C
270o rotation matrtix
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2) Rotations
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2) Rotations

• Example 2  The matrix below represents the
  vertices of a polygon. Write a matrix to
  represent the vertices after a rotation of 90o.

A B C D
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2) Rotations

• Example 2  The matrix below represents the
  vertices of a polygon. Write a matrix to
  represent the vertices after a rotation of 90o.

A B C D
90o rotation matrtix
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2) Rotations

• Example 2  The matrix below represents the
  vertices of a polygon. Write a matrix to
  represent the vertices after a rotation of 90o.

A B C D
A B C D
90o rotation matrtix
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Homework

• Create some way to remember the 8 matrices used
  for reflections and rotations.
• You are responsible for knowing all 8.
• The matrices are located on p.193 and p.194
• 2) p.196 10, 11, 13, 14, 18-21, 31, 32
• 3) QUIZ WEDNESDAY section 4.4