Geometry

Question Analysis

This question involves transformation notation. The main focus is on identifying which transformation will map a quadrilateral that is symmetric with respect to the origin onto itself.

Key Concept Explanation

Transformations such as rotation ( where is the center of rotation and is the angle of rotation), dilation ( where is the center of dilation and is the scale factor)  are used. A figure symmetric about the origin has the property that for every point on the figure, the point is also on the figure.

Step-by-Step Solution

1. Analyze each transformation:

A.For a rotation ,  rotating a point 225 degrees counter - clockwise around the origin will change the position of the points of the quadrilateral and not map it onto itself.

B.For a dilation followed by a 45 - degree rotation, the dilation by 1 keeps the size the same, but the 45 - degree rotation will change the orientation of the quadrilateral, so it will not map onto itself.

C.For a dilation

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