2-4 Modeling Motion with Matrices

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2-4 Modeling Motion with Matrices

• Pre Calc A

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Vocabulary

• Transformations
• Translation
• Reflection
• Rotations
• Dilations

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Ex 17

• Suppose quadrilateral RSTU with vertices R(3, 2),
  S(7, 4), T(9, 8) and U(5, 6) is translated 2
  units right and 3 units down.
• a. represent the vertices of the
• quadrilateral as a matrix
• b. write the translation matrix
• c. use the translation matrix to find
• the vertices of RSTU
• d. Graph the pre-image and image

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Ex

• A parallelogram has vertices W(-2, 4), X(0, 8),
  Y(4, 6), and Z(2, 2). Find the coordinates of the
  dialted parallelogram WXYZ for a scale factor
  of 1.5. Describe the dilation.

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Reflections
Reflection over the Symbolized by Multiply the vertex matrix by
x-axis Rx-axis
y-axis Ry-axis
Line yx Ryx
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Ex

• A triangle has vertices A(-1, 2), B(4, 4) and
  C(3, -2). Find the image of the triangle after a
  reflection over the y-axis.

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Rotations
For a counterclockwise rotation about the origin Symbolized by Multiply the vertex matrix by
90 Rot90
180 Rot180
270 Rot270
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Ex last one

• A triangle has vertices A(-1, 2), B(4, 4) and
  C(3, -2). Find the image of the triangle after a
  rotation of 90 about the origin.