Geometry

Question Analysis

The question focuses on identifying the transformation that maps a quadrilateral, which is symmetric about the origin, onto itself, testing knowledge of rotation, dilation, and reflection notations.

Key Concept Explanation

Rotation (): Rotates a figure around the origin by an angle .

Dilation (): Changes the size of a figure with the origin as the center, where is the scale factor. A negative flips the figure across the origin.

Reflection: Flips a figure across a line, altering its orientation.

Step-by-Step Solution

1. Analyze each option:

A.For and , the rotation changes the orientation and the dilation changes the size, so it won't map the quadrilateral onto itself.

B.A reflection across the line

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