
These are general terms that you will see in your study of transformations.
Remember that transformations are operations that alter the form of a figure.
The standard transformations are reflections, translations, rotations, and dilations.
Terms are listed in alphabetical order.
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' (referred to as P prime), then P' is called the image of point P under the reflection (or the preimage). Such a transformation is denoted r_{l} (P) = P'. 

Invariant: A figure or property that remains unchanged under a transformation of the plane is referred to as invariant (not varying). 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 xaxis, 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".)


Rigid Transformation (or Isometry): A rigid transformation, or isomentry, is a transformation of the plane that preserves length. For example, if the sides of an original preimage 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 nondirect or opposite isometry changes the order (such as clockwise changes to counterclockwise). 
Transformation: A transformation of the plane is a onetoone mapping (or moving) of points in the plane to points in the plane. In the plane, a mapping will carry ordered pairs to new locations according to some specified rule. 
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 to arrive at its conclusion. 
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