To determine which mapping corresponds to a 270-degree (counterclockwise) rotation, we can analyze how the coordinates (x, y) transform.
A 270-degree counterclockwise rotation can also be described as a 90-degree clockwise rotation. The effect of a 90-degree clockwise rotation on the coordinates (x, y) is to transform them to (y, -x).
Now, let's look at the options provided:
A. (x,y) → (-y,x)
B. (x,y) → (y,-x)
C. (x,y) → (-x,-y)
D. (x,y) → (-y,-x)
From the analysis, we see that:
- Option B, \( (x, y) → (y, -x) \), is the correct mapping for a 270-degree counterclockwise rotation.
Thus, the answer is B. (x,y) → (y, -x).
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