Review of Transformations - Notations and Formulas Topic Index | Geometry Index | Regents Exam Prep Center

 Line Reflections
A reflection is a flip.  It is an opposite isometry - the image does not change size but the lettering is reversed.

 Reflection in the x-axis: When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite.      or Reflection in the y-axis: When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite.      or Reflection in y = x: When you reflect a point across the line y = x, the x-coordinate and the y-coordinate change places.        or Reflection in y = -x: When you reflect a point across the line y = -x, the x-coordinate and the y-coordinate change places and are negated (the signs are changed).     or

 Point Reflections
A point reflection exists when a figure is built around a single point called the center of the figure.  It is a direct isometry.

 Reflection in the Origin: While any point in the coordinate plane may be used as a point of reflection, the most commonly used point is the origin.     or

 Rotations
(assuming center of rotation
to be the origin)
A rotation turns a figure through an angle about a fixed point called the center.  A positive angle of rotation turns the figure counterclockwise, and a negative angle of rotation turns the figure in a clockwise direction.  It is a direct isometry.
 Rotation of 90°: Rotation of 180°: (same as point reflection in origin) Rotation of 270°:

 Dilations
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size NOT an isometryForms similar figures.
 Dilation of scale factor k: The center of the dilation is assumed to be the origin unless otherwise specified.

 Translations
A translation "slides" an object a fixed distance in a given direction.  The original object and its translation have the same shape and size, and they face in the same direction.  It is a direct isometry.

 Translation of  h, k:

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