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20 Cards in this Set
- Front
- Back
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Line Reflection
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Order of points is reversed
(clockwise -> counterclockwice, v.v.) |
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Point Reflection
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Order of points is preserved
Length of points is preserved |
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Rotation
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R<M>90*(A)= A rotated 90*s counter clockwise
R<M>-90*(A)= A rotated 90*s clockwise Order preserved Length preserved |
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Translation
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T <(a,b)>(x,y)=(x+a, y+b)
Order preserved Length preserved |
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Dilation
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D<k>(x,y)=D(kx, ky)
Order preserved Length changed |
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Isometry
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A transformation that preserves distance [length]
-line reflection -rotation -point rotation -translation NOT: -dilation |
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Indirect/ Opposite Isometry
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A transformation that has an odd number of line reflections
// ORDER OF VERTICES IS REVERSED (clockwise->counter clockwise, v.v.) - Line reflection |
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Direct Isometry
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ORDER OF VERTICES IS PRESERVED
-Rotation -Point rotation translation |
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SPECIAL PROPERTY OF:
2 line reflections on 2 intersecting lines [a figure reflected twice over perpendicular lines] |
The angle between the 2 intersecting lines is half equivalent to the angle of rotation
(If they are rotated by 60*s, the angle at the intersection will be 30*s |
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SPECIAL PROPERTY OF:
2 line reflections on 2 parallel lines [a figure reflected twice over parallel lines] |
Equivalent to a translation perpendicular to parallel lines.
- The translation length is double the distance between the 2 lines (original line and line after 2 reflections) |
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SPECIAL PROPERTY OF:
Glide Reflection |
-First, line reflection, then translation
translation is perpendicular to the lined of reflection |
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RULE:
r<x>(x,y)= |
r<x>(x,y)=(x, -y)
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RULE:
r<y>(x,y)= |
r<y>(x,y)=(-x,y)
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RULE:
r<y=x>(x,y)= |
r<y=x>(x,y)=(y,x)
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RULE:
R<o>(x,y)= AND equivalent transformations |
R<o>(x,y)=(-x,-y)
equivalent transformations r<x> o r<y>(x,y)=(-x,-y) r<y> o r<x>(x,y)=(-x,-y) R<O, 180*>(x,y)=(-x,-y) |
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RULE:
R<90*>(x,y)= |
R<90*>(x,y)=(-y,x)
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RULE:
R<180*>(x,y)= |
R<180*>(x,y)=(-x,-y)
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RULE:
R<270*>(x,y)= |
R<270*>(x,y)=(y,-x)
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HOW TO GRAPH A PARABOLA:
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solve for points allowed by inequality
make x|y chart plot points |
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HOT TO GRAPH AN IVH:
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xy=k
solve for points between -k and k make an x|y chart plot points |
