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

 

Examples:

1)      Dot paper

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2)      Coordinate axes

 

 

 

 

 

 

 

 

 

 

 

 

Example

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure

Half-turn—rotation of 180°

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Rotations

 

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