Geometry: Transformations: Translations

Objectives

• Students will identify a translation as an isometry, also called a congruence transformation.
• Students will identify which properties (side length, angle measure, perimeter, area, and orientation) of a figure are preserved in a translation and which are not.
• Students will generalize the relationship between the coordinates of a pre-image and its image in a translation in the coordinate plane.

Vocabulary

• pre-image
• image
• transformation
• translation
• congruent figures
• congruence transformation
• isometry

About the Lesson

In this lesson students will investigate the meaning of a translation, and they will discover which properties are preserved in a translation and which are not. They will identify and generalize the coordinates of a triangle under translations in the coordinate plane. As a result, students will:

• Translate a triangle in horizontal and vertical directions to develop their visualization and special sense of a translation.
• Describe the consequences of the translation in terms of identifying those properties which are preserved and those which are not, and identify and generalize the coordinates of translations in the coordinate plane.
• Infer that a translation does not alter any of the measurements of a translated object and as such, a translation is an example of an isometry, or congruence transformation.