1.2.3 Exploring Transformations Key Objectives
• Apply transformations to points and functions. • Interpret transformations of real-world data. Key Terms • A transformation is a change in position or size of a figure.
• An image is a shape that results from a transformation of a figure known as the preimage . • A translation , or slide, is a transformation that moves every point of a figure the same distance and direction. • A reflection is a transformation across a line, called the line of reflection, that results in a mirror image. Each point and its image are the same distance from the line of reflection. • A compression is a transformation that pushes the points of a graph horizontally toward the y -axis or vertically toward the x -axis. • A stretch is a transformation that pulls the points of a graph horizontally away from the y -axis or vertically away from the x -axis. Example 1 Translating Points A translation is a transformation where each point in a figure is moved the same distance in the same direction. When a figure is translated left or right, called a horizontal translation, each point shifts left or right by a number of units and each of the figure’s x -coordinates changes by that number of units. When a figure is translated up or down, called a vertical translation, each point shifts up or down by a number of units and each of the figure’s y -coordinates changes.
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