geometry chapter 9 vocab
Terms
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- 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.
- column matrix
- a matrix containing one column often used to represent an ordered pair or vector.
- component form
- a vector expressed as an ordered pair.
- composition
- a transformation made up of successive transformations.
- 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 ray CP such that CP'= IkI times cp. When k < 0, the image P' of P is the point on the ray opposite of ray cp such that CP' = k times CP.
- direct isometry
- an isometry in which the image of a figure is found by moving the figure intact within the plain.
- 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
- glide reflections
- a composuition of a translation and a reflection in a line parallel to the direction of the translation.
- indirect isometry
- an isometry that cannot be preformed by maintaining their orientation of the points an in a direct isometry
- isometry
- a mapping for which the original figure and its image are congruent.
- line of reflection
- a line through a figure that separated the figure into two mirror images.
- line of symmetry
- a line that can e drawn through a plane figure so that the figure on one side is the reflection image of the figure on the oppsite side
- magnitude
- the length of a vector
- parallel vectors
- vectors that have the same 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 matrix of a figure to find the coordinates of the reflected image.
- regular tessellaiont
- a tessellation formed by only one type of regular polygon.
- resultant
- the sum of two vectors
- rotation
- a transformation that turns every point of a preimage 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 vertes matrix of a figure to find the corrdinates of the rotated image.
- 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.
- scalar
- A constant multiplied by a vector
- scalar multiplicatication
- Multiplication of a vector by a scalar
- semi-regular tessellation
- A uniform tessellation formed using two or more regular polygons
- similarity transfrmation
- 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 re-image point
- translation
- A transformation that moves all points of a figure the same distance in the same direction.
- translation matrix
- A matrix that can be added to the vertex matrix of a figure to find the coordinates of the translated image.
- 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 represents a polygon by placing all of the column matrices of the coordinates of the vertices into one matrix.