Transcript 2-4 Modeling Motion with Matrices

2-4 Modeling Motion with
Matrices
Pre Calc A
Vocabulary
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Transformations
Translation
Reflection
Rotations
Dilations
Ex 17:
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y
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 R’S’T’U’
d. Graph the pre-image and image
Ex
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:
A parallelogram has vertices W(-2, 4), X(0, 8), Y(4, 6), and Z(2,
2). Find the coordinates of the dialted parallelogram W’X’Y’Z’ for
a scale factor of 1.5. Describe the dilation.
Reflections
Reflection over the:
Symbolized by:
Multiply the vertex matrix by:
x-axis
Rx-axis
1 0 
0 1


y-axis
Ry-axis
  1 0
 0 1


Line y=x
Ry=x
0
1

1
0
Ex
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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.
Rotations:
For a counterclockwise
rotation about the origin:
Symbolized by:
Multiply the vertex matrix by:
90˚
Rot90
0  1
1 0 


180˚
Rot180
 1 0 
 0  1


270˚
Rot270
 0 1
  1 0


Ex last one:
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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.