General "Transformation" Vocabulary
Geometry Index | Regents Exam Prep Center


The following vocabulary terms will appear throughout the lessons in the section on Transformational Geometry.


Image:
 
An image is the resulting point or set of points under a transformation.  For example, if the reflection of point P in line l is P', then P' is called the image of point P under the reflection.  Such a transformation is denoted rl (P) = P'.


Isometry:
 An isometry is a transformation of the plane that preserves length.  For example, if the sides of an original pre-image triangle measure 3, 4, and 5, and the sides of its image after a transformation measure 3, 4, and 5, the transformation preserved length. 
             A direct isometry preserves orientation or order - the letters on the diagram go in the same clockwise or counterclockwise direction on the figure and its image.
             A non-direct or opposite isometry changes the order (such as clockwise changes to counterclockwise).


Invariant:
  A figure or property that remains unchanged under a transformation of the plane is referred to as invariant.  No variations have occurred.
 

Opposite Transformation:  An opposite transformation is a transformation that changes the orientation of a figure.  Reflections and glide reflections are opposite
transformations. 

For example, the original image, triangle ABC, has a clockwise orientation - the letters A, B and C are read in a clockwise direction.  After the reflection in the x-axis, the image triangle A'B'C' has a counterclockwise orientation - the letters A', B', and C' are read in a counterclockwise direction.

A reflection is an opposite transformation.


Orientation:
  Orientation refers to the arrangement of points, relative to one another, after a transformation has occurred.  For example, the reference made to the direction traversed (clockwise or counterclockwise) when traveling around a geometric figure. 
                        (Also see the diagram shown under "Opposite Transformations".)

Counterclockwise

Clockwise

 


Position vector:  A position vector is a coordinate vector whose initial point is the origin.  Any vector can be expressed as an equivalent position vector by translating the vector so that it originates at the origin.


Transformation:  A transformation of the plane is a one-to-one mapping of points in the plane to points in the plane.


Transformational Geometry:  Transformational Geometry is a method for studying geometry that illustrates congruence and similarity by the use of transformations.


Transformational Proof:  A transformational proof is a proof that employs the use of transformations.


Vector:
  A quantity that has both magnitude and direction; represented geometrically by a directed line segment.