Geometry Vocab 2

36 terms

Line of reflection

a line through a figure that separates the figure into two mirror images

Line of symmetry

a line that can be drawn through a plane figure so that the on one side is the reflection image of the figure on the opposite side.

Magnitude

the length of the vector

Parallel vectors

vector that have the same or opposite direction

Point of symmetry

the common point of reflection for all points of a figure

reflection

a transformation representing a flip of the figure over a point, line, or plane

Reflection matrix

a matrix that can be multiplied by the vertex of a figure to find the coordinates of the reflected image

resultant

the sum of two vectors

rotation

a transformation that turns every point of image through a specified angle and direction about a fixed point, called the center of rotation

rotation matrix

a matrix that can be multiplied by the vertex matrix of a figure to find the coordinates of the rotated image

rotational symmetry

if a figure can be less than 360 about a point so that the image and the pre image indistinguishable the figure has rotational symmetry

scalar

a constant multiplied by a vector

semi-regular tessellation

a uniform tessellation formed using two or more regular polygons

similarity transformation

when a figure and its transformation image are similar

standard position

when the initial point of a vector is at the origin

tessellation

a pattern that covers a plane by transforming the same figure or set of figures so that there are no overlapping or empty spaces

transformation

in a plane, a mapping for which each point has exactly one image point and each image point has exactly one per-image point.

translation

a transformation that moves all points of a figure the same distance in the same direction.

Uniform

tessellations containing the same arrangement of shapes and angles at each vertex.

vector

A directed segment representing a quantity that has both magnitude, or length, and direction.

vertex matrix

A matrix that represented a polygon by placing all of the column matrix of the coordinate of the vertices into one matrix.

Angle of rotation

the angle between the line of sight and the horizontal when an observer looks downward.

Center of rotation

a fixed point around which shapes move in a circular motion to a new position.

column matrix

a matrix containing one column often used to represent an ordered pair or a vector, such as (x,y)=x/y

component form

a vector expressed as an ordered pair, change in x, change in y.

composition of reflection

successive reflections in parallel lines.

dilation

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 CP such that CP'=k times CP. When k <0, the image P' of P is the point on the ray opposite segment CP such that CP' = k times CP.

direct isometry

an isometry in which the image of figure is found by moving the figure intact within the plane.

Direction

the measure of the angle that a vector forms with the positive x axis or any other horizontal line.

Equal vectors

vectors that have the same magnitude and direction.

Glide reflection

a composition of a translation and a reflection in a line parallel to the direction of the translation.

Indirect isometry

an isometry that cannot be performed by maintaining the orientation of the points, as in a direct isometry.

Isometry

a mapping for which the original figure and its image are congruent.

translation matrix

a matrix that can be added to the vertex matrix of a figure to find the coordinate of the translation.

scalar

a constant multiplied by a vector

scalar multiplication

multiplication of a vector by a scalar