Chapter 9 Flashcards
Rotations about the origin
180 degrees
(x,y) —> (-x,-y)
Rotations about the origin
270 degrees clockwise or
90 degrees counterclockwise
(X,Y) –> (-Y, X)
Rotations about the origin
90 degrees clockwise or 270 degrees counterclockwise
(x,y) —> (y,-x)
Reflections over the y-axis
(x,y) —> (-x,y)
Reflections over x-axis
(x,y) —> (x,-y)
Reflections over the y=x
(x,y) —> (y,x)
Rotation about the origin means…
Counterclockwise
Angle of rotation
The angle through which a preimage is rotated to form the image
Center of rotation
A fixed point around which shapes move in a circular motion to a new position
Composition of transformation
The resulting transformation when a transformation is applied to a figure and then another transformation is applied to its image
Glide reflection
The composition of a translation followed by a reflection in a line parallel to the translation vector.
Line of reflection
A line in which each point on the preimage and its corresponding point on the image are the same distance from this line
Line of symmetry
A line that can be drawn through a plane figure so that the figure on one side is the reflection image of the figure on the opposite side
Magnitude of symmetry
The smallest angle through swhich a figure can be rotated so that it maps into itself
Order of symmetry
The number of times a fugure can map into itself as it rotates from 0 degrees to 360 degrees
Plane symmetry
Symmetry in a three-dimensional figure that occurs if the figure can be mapped into itself by a reflection in a plane
Rotational symmetry
If a figure can be rotated less than 360 degrees about a point so that the image and the preimage are indistinguishable, the figure has rotational symmetry.
Symmetry
A figure has symmetry if there exists a rigid motion- reflection translation rotation or glide reflection that maps the figure into itself
Translation vector
The vector in which a translation maps each point to its image.
Order
How many times it matched up during a full rotation
Number of sides
Magnitude
The smallest angle through which a figure can be rotated do it maps into itself
Magnitude= 360/order
