Geometry

Question Analysis

The question focuses on understanding the combined effect of two geometric transformations, dilation with a scale factor of - 1 and a 180 - degree rotation, on a quadrilateral, testing knowledge of transformation notations and their cumulative impact.

Key Concept Explanation

Dilation (): A dilation with center and scale factor changes the size and, when k < 0, the orientation of a figure. For , each point is mapped to .

Rotation (): A rotation about the origin by an angle changes the orientation of the figure. For ,  each point is also mapped to .

Step-by-Step Solution

1. Let a point on the quadrilateral be .

2. After the dilation , the point

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