To determine which mapping corresponds to a 90-degree counterclockwise rotation about the origin, let's analyze the transformations.
A 90-degree counterclockwise rotation converts a point \((x, y)\) into the point \((-y, x)\).
Now, let's examine each of the proposed mappings:
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(xy) - (-x): This does not represent a transformation of points \((x, y)\). Instead, it seems to describe a mathematical expression.
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(x, y) → (y, x): This mapping simply swaps the coordinates but does not account for the rotation. Therefore, this is not the correct transformation.
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(x, y) → (x, y): This represents no change at all. Clearly, it is not the transformation we are looking for.
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(xy)(y - x): Similar to option 1, this does not represent a standard transformation of coordinates but looks more like an expression as well.
From the options you provided, it appears none of them correctly provide the transformation for a 90-degree counterclockwise rotation about the origin. The correct transformation would be \((x, y) \to (-y, x)\).
If you meant to include that option or need something specific within the selections provided, please check again.