Geometry

Question Analysis

This question focuses on using transformation notation to determine which transformation will map a quadrilateral, symmetric about the origin, onto itself. The key is understanding how different transformations affect the position and orientation of the figure.

Key Concept Explanation

Rotations (): Rotate a figure around the origin by an angle . Different angles change the figure's orientation.

Dilations (): Change the size of a figure with the origin as the center. The scale factor determines the extent of the change. A negative scale factor also flips the figure's orientation.

Reflection: Flips a figure across a line, altering its position and orientation relative to that line.

Step-by-Step Solution

1. Analyze each option:

A.For a reflection across the line , points become . This changes the orientation of the quadrilateral and  won't map it onto itself if it's symmetric only about the origin.

B.For a dilation , each point

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