geometry m1 tC
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| basic rigid motion | transformations that preserve lengths of segments and measures of angles
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| composition of transformations | preforming multiple transformations in succession
ex : ry−axis∘R90
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| dilation | a transformation that preserves angle measures but not the lengths of segments
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| direct isometry | an isometry that preserves orientation
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| image | the figure that has undergone the transformation
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| isometry | a transformation that preserves distance
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| line reflection | a transformation across a line, called the line of reflection, so that the line of reflection is the perpendicular bisector of each segment joining a point and its image
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| line reflection notation | A'= (ry−axis(A))
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| opposite isometry | an isometry that changes orientation
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| pre-image | a figure before a transformation is preformed on it
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| regular polygon | a polygon with all sides of equal length and all interior angles of equal measure. it is equilateral and equiangular
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| rotation | a transformation that maps every point by rotating the plane or given angle around a fixed point called the center of rotation
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| rotation notation |
R180 ∘ (x,y)
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| translation | a transformation where all the points of a figure are moved the same distance in the same direction
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| translation notation | T a,b (A) = A'
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| rotational symmetry of a figure | a nontrivial rotational symmetry of a figure is a rotation of the plane that maps the figure back to itself such that the rotation is greater than 0 degrees but less than 360 degrees
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| the formula for the angle of rotational symmetry | 360
_____________
# of sides
of a regular
polygon
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| what happens when you reflect a point P(x,y) over the y-axis | P'= (-x,y)
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| what happens when you reflect a point P(x,y) over the x-axis | P'=(x,-y)
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| what happens when you reflect a point P(x,y) over the line y=x | P'=(y,x)
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| what happens when you reflect a point P(x,y) over the line y=-x | P'= (-y,-x)
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| what happens when you reflect a point P(x,y) over the origin | P' = (-x,-y)
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| How do you translate a point P(x,y) 'a' units horizontally and 'b' units vertically | P'=( x+ a, y+ b)
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| Postive angles are preformed in a _____________ direction | counterclockwise
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| Negative angles are preformed in a _____________ direction | clockwise
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