When a point \((x, y)\) is rotated 90 degrees counterclockwise about the origin, the coordinates transform according to the following mapping:
\[ (x, y) \to (-y, x) \]
However, none of the options you provided directly match this. Let's evaluate the given options to see which one resembles the transformation:
- \((xy) - (y-x)\) - This option doesn't represent a mapping of points in a coordinate system.
- \((x, y) \to (y, x)\) - This is a switch of the x and y coordinates (reflection over the line y=x), not a rotation.
- \((x, y) \to (x, y)\) - This keeps the point unchanged, which is not a rotation.
- \((x, y) \to (y, -x)\) - This option closely resembles a 90-degree counterclockwise rotation, but is actually the mapping for a 90-degree clockwise rotation.
Therefore, evaluating the transformations, it appears none correctly describe a 90-degree counterclockwise rotation. However, please double-check if the structure has changed in terms of placement, as the closest indicated is following the format of transformation before correction. As described \((x, y) \to (-y, x)\) fits the expected trajectory.
Make sure to refer back to the original instructions given that you need a function from the provided set or structure if there are any updates or corrections needed in the specified notation.
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