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