To determine which mapping corresponds to a 270-degree counterclockwise rotation, we can start by noting the effect of such a rotation on the coordinates of a point \((x, y)\).
A 270-degree counterclockwise rotation can also be thought of as a 90-degree clockwise rotation. The transformation for a 90-degree clockwise rotation from \((x, y)\) to \((y, -x)\) applies here.
Thus, from \((x, y)\):
- For a 270-degree counterclockwise rotation, the mapping becomes \((x, y) \to (y, -x)\).
Now let's analyze the given options to see which one matches this transformation.
- (2, g) → (-y, -2): This does not correspond to the rotation as it flips both axes.
- (2, y) → (-y, a): This does not match the expected output of \((y, -x)\).
- (z, y) → (-y, y): This is incorrect since it does not rearrange the coordinates as needed.
- (z, y) → (-y, -x): This would imply a reflection and a rotation, which does not match the 90-degree clockwise transformation.
Looking through the options, none of them exactly match \((y, -x)\). However, it's likely that the closest option or the intended transformation was meant to describe a 270-degree rotation.
If we consider the correct transformation being missed, let’s re-check if any combination reflects an implicit transformation. Although, without additional exact options that match \((y, -x)\), none of these mappings seem to correctly define the 270-degree counterclockwise rotation.
If you have additional context or corrections in provided options, please clarify for an accurate choice.
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