7 Linear Transformations
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Last updated 9:41 AM on 10/24/22
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10 Terms
1
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Reflection in the y-axis
-1 0
0 1
0 1
2
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Invariant points/lines
of a reflection in the y-axis
of a reflection in the y-axis
Points on the y-axis are invariant points
The lines x=0 and y=k for any value of of k are invariant lines
The lines x=0 and y=k for any value of of k are invariant lines
3
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Reflection in the x-axis
1 0
0 -1
0 -1
4
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Invariant points/lines of a reflection in the x-axis
Point on the x-axis are invariant points
The lines y=0 and x=k for any value of k are invariant lines
The lines y=0 and x=k for any value of k are invariant lines
5
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Reflection in the line y=x
0 1
1 0
1 0
6
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Invariant points/lines of a reflection in the line y=x
Points on the line y=x are invariant points
The lines y=x and y=-x+k for any value of k are invariant lines
The lines y=x and y=-x+k for any value of k are invariant lines
7
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Reflection in the line y=-x
0 -1
-1 0
-1 0
8
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Invariant points/lines of a reflection in the line y=-x
Points on the line y=-x are invariant points
The lines y=-x and y=x+k for any value of k are invariant lines
The lines y=-x and y=x+k for any value of k are invariant lines
9
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Matrix representing a rotation anti-clockwise about the origin
Cos(x) -sin(x)
Sin(x) cos(x)
Sin(x) cos(x)
10
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The transformation represented by a 0
0 b
0 b
Stretch of scale factor a parallel to the x-axis and scale factor y parallel to the y-axis