Algebra 1 Notes Lesson 4-2: Transformations on the Coordinate Plane

Mathematics Standards Number, Number Sense and Operations: Demonstrate fluency in computations using real numbers. Geometry and Spatial Sense: Identify the reflection and rotation symmetries of two- and three-dimensional geometric figures. Geometry and Spatial Sense: Perform reflections and rotation using compass and straightedge constructions and dynamic geometry software.

Mathematics Standards Geometry and Spatial Sense: Derive coordinate rules for translations, reflections and rotations of geometric figures in the coordinate plane. Geometry and Spatial Sense: Show and describe the results of combinations of translations, reflections and rotations (compositions). Geometry and Spatial Sense: Analyze two-dimensional figures in a coordinate plane.

Vocabulary Transformation – Movement of figures Preimage –image before a transformation Image – Image after a transformation

We will always flip figures over the x-axis or y-axis Reflection A figure is flipped over a line. We will always flip figures over the x-axis or y-axis

Translation A figure is slid in any direction. To translate a point by an ordered pair (a, b), add a to the x-coordinate and b to the y-coordinate. You can also count on a graph.

Dilation A figure is enlarged or reduced. To dilate a figure by a scale factor k, multiply both coordinates by k. If k > 1, the figure is enlarged. If k < 1, the figure is reduced.

Rotation A figure is turned around a point. To rotate a figure 90º counterclockwise about the origin, switch the coordinates of each point and then multiply the new first coordinate by -1. To rotate a figure 180º about the origin, multiply both coordinates of each point by -1.

Example 1 Identify each transformation. a)

Example 1 Identify each transformation. a) translation b) dilation

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