13.1 Translations and Rotations


Def. Translations—a motion of the plane that moves every point of the plane a specified distance in a specified direction along a straight line.



Properties of Translations

  1. A figure and its image are congruent.
  2. The image of a line is a line parallel to it.





Constructions of Translations



1)      Dot paper

















2)      Coordinate axes














Find the coordinates of the image of quadrilateral ABCD in Figure under the translation in parts a-c.  Draw the image in each case.

























Half-turn—rotation of 180°





















Def. Rotation—a transformation of the plane determined by holding one point –the center—fixed and rotating the plane about this point by a certain amount in a certain direction.


Example  –rotate counter-clockwise 90° about O