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Geometry

How can a geometric figure be translated is given.

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After completing this tutorial, you will be able to complete the following:

- Perform a translation (slide) of geometric figures represented on graph paper.

Transformations that create images that are congruent to the original figure are called rigid transformations.

Rigid transformations or isometries, come from the Greek phrases isometry, meaning equal measure. There are three basic isometries: translations, reflections, and rotations.

All three of these are considered isometric because they preserve congruence. In other words, a transformation in which the original figure and translated figure have the same side lengths and angle measurements is considered to be isometric.

Translations maintain congruence and preserve the figure's original orientation.

A translation is a slide. The figure is simply moved from its original space without changing the figure's orientation.

The blue figure is the original figure. The red figure represents the slide or translation and it is called image. Notice how the red figure appears exactly as the blue figure with the point at the top of the figure. This means it retains its original orientation. A translation is a specific type of transformation, or change, in an original figure, in which an image is formed by moving every point on a figure the same distance in the same direction.

To create a translation, every point of the shape must move the same distance and in the same direction.

In order to create a correct translation, every point of the figure must be moved so that all vertices (or corners) of the figure are moved. A translation preserves congruence and orientation so that any point that is not moved correctly will change the figure's shape.

Example:

Each point is moved in a specific direction and number of spaces. In this case, all of the points are moved three units to the right and two units down. Once all of the points are moved a translated figure is created. The new figure is congruent to the original one and maintains the same orientation because all of the points were moved the same number of spaces and in the same direction.

Approximate Time | 15 Minutes |

Pre-requisite Concepts | Students should know the definitions of point, line, intersecting line, translation, slide, and transformation. |

Course | Geometry |

Type of Tutorial | Skills Application |

Key Vocabulary | translation, image, grid paper |