A 90-degree clockwise rotation about the origin can be represented by the transformation \( (x, y) \mapsto (y, -x) \). To determine which of the given options corresponds to this transformation, we can analyze each one:
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A reflection over the line \( y = x \): This transformation maps \( (x, y) \) to \( (y, x) \), which is not the same as a 90-degree clockwise rotation.
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A 270 degrees counterclockwise rotation: This transformation can be represented as \( (x, y) \mapsto (-y, x) \). To check equivalency, note that a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation. Thus, this is the correct mapping.
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A dilation with a scale factor of 1/4: This transformation scales a point \( (x, y) \) to \( \left(\frac{x}{4}, \frac{y}{4}\right) \), which does not involve rotation. Hence, it's not equivalent.
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A translation: A translation shifts a point by adding constants to its coordinates, which does not represent a rotation.
Based on the analysis, the correct answer is:
A 270 degrees counterclockwise rotation.