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