# Honors Geometry Companion Book, Volume 1

1.2.3 Transformations in the Coordinate Plane Key Objectives

• Identify reflections, rotations, and translations. • Graph transformations in the coordinate plane. Key Terms • A transformation is a change in position, size, or shape of a figure. • A reflection (or flip ) is a transformation across a line, called the line of reflection. Each point and its image are the same distance from the line of reflection. • A translation (or slide ) is a transformation in which all the points of a figure move the same distance in the same direction. • A rotation (or turn ) is a transformation about a point P , called the center of rotation. Each point and its image are the same distance from P .

• The original figure in a transformation is called the preimage . • The resulting figure in a transformation is called the image .

When a figure is changed in terms of its position, size, or shape, this change is called a transformation. Three types of transformations are reflections, translations, and rotations. In a transformation, the original figure, called the preimage, is mapped to a new figure, called the image. A transformation from a preimage to an image can be described using arrow notation where the image and preimage are named using the same point names, but with a prime symbol (′) added after each point for the image name.

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