Angle of rotation
angle formed by rays drawn from the center of rotation to a point and its image
Center of rotation
the point about which a figure is rotated
a matrix with only one column
written form of a vector that combines the horizontal and vertical components <5,3>
a transformation made up of successive transformations
a transformation determined by a center point C and a scale factor k. when k>0, the image P' of P is the point on line CP such that CP' = |k| X CP. When k=0, the image P' of P is the point on the ray opposite line CP such that CP' = k X CP
a transformation that preserves distance and orientations
the measure of the angle that a vector forms with the positive x-axis or any other horizontal line
two vectors that have the same magnitude and same direction
A combination of a translation and a reflection.
An isometry that cannot be performed by maintaining the orientation of the points, as in direct isometry.
equality of measure (e.g., equality of height above sea level or equality of loudness etc.)
line of reflection
The line over which a figure is reflected. The vertices of the original and new figure are the same distance from this.
line of symmetry
a line that divides a figure into two halves that are mirror images of each other
the length of a vector
vectors that have the same or opposite direction
point of symmetry
every point on the figure on the opposite side of and equally distant from a central point
a transformation representing a flip of the figure over a point, line, or plane
A matrix that can be multiplied by the vertex matrix of a figure to find the coordinate of the reflected image.
A regular polygon is repeated to fill a plane.
a vector that is the sum of two or more other vectors
a single complete turn (axial or orbital)
the ability to rotate the figure around some point so that it concides with itself
transformation used to rotate the figure
a constant multiplied by a vector
the multiplication of each entry in a matrix by the same number
2 or more polygons are repeated to fill plane and vertices are identical
it maps figures into similar figures
when the initial point of a vector is at the origin
a repeating pattern of plane figures that completely cover a plane with no gaps or overlaps
in a plane, a mapping for which each point has exactly one image point and each image point has exactly one preimage point
a transformation that moves all points of a figure the same distance in the same direction
a matrix that represents a translated figure
tessellations containing the same arrangement of shapes and angles at each vertex
a directed segment representing a quantity that has both magnitude, or length, and direction
a matrix where all vertices of a polygon are placed in one matrix