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Properties of Isometries
Honors Geometry Chapter 9
14
Mathematics
9th Grade
04/01/2014

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Term
90 rotation counterclockwise about the origin
Definition
(x, y) -> (-y, x)
Term
180 rotation counterclockwise about the origin
Definition
(x, y) -> (-x, -y)
Term
270 rotation counterclockwise about the origin
Definition
(x, y) -> (y, -x)
Term
Reflection across the line y=x
Definition
(x, y) -> (y, x)
Term
Reflection across the y-axis
Definition
(x, y) -> (-x, y)
Term
Reflection across the x-axis
Definition
(x, y) -> (x, -y)
Term
Dilation centered at the origin where the scale factor is k
Definition
(x, y) -> (kx, ky)
Term
Isometry
Definition
A mapping for which the original figure and its image are congruent, has a scale factor of 1
Term
Axis of Symmetry
Definition
Symmetry in a 3-D figure that occurs if the figure can be mappped onto itself by a rotation between 0 and 360 degrees in a line
Term
Plane Symmetry
Definition
Symmetry in a 3-D figure that occurs if the figure can be mapped onto itself by a reflection in a plane
Term
Magnitude of Symmetry
Definition
The angle of rotation that is the smallest angle through which a figure can be rotated so that it maps onto itself. It is found by dividing 360/order.
Term
Order of Symmetry
Definition
The number of times a figure maps onto itself as it rotates from 0 to 360
Term
How many lines of symmetry does a regular n-gon have?
Definition
n lines of symmetry. A regular polygon has the same number of lines of symmetry as it does sides.
Term
What is the angle of rotation for a figure reflected in two lines that intersect to form an angle of x degrees?
Definition
2x
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