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 to understand how different transformations (rotations and dilations) affect the position and orientation of the quadrilateral.

 

Key Concept Explanation

Rotations:  rotates a figure around the origin  by an angle . Positive angles are counter - clockwise rotations.

Dilations:  changes the size of a figure with the origin  as the center of dilation. If , the figure's size remains the same; if k> 1 or k < - 1,  it is enlarged; if - 1<k < 1,, it is reduced. A negative scale factor also reflects the figure across the origin.

 

Step-by-Step Solution

1. Analyze each option:

A.For : A 180 - degree rotation around the origin maps a point  to . Since the quadrilateral  is symmetric about the origin,  every point  on the quadrilateral has a corresponding point

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