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6 of 116 of 11 Items Question A figure is rotated 90 degrees counterclockwise about the origin. Which of the following function mappings was applied? (1 point) Responses Option #1: (x,y)→(y,−x) Option #1: (x,y)→(y,−x) Option #2: (x,y)→(−y,x) Option #2: (x,y)→(−y,x) Option #3: (x,y)→(−x,−y) Option #3: (x,y)→(−x,−y) Skip to navigation page 1 of 1
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GPT-4o mini
To determine which function mapping corresponds to a 90-degree counterclockwise rotation about the origin, we can analyze the transformations provided.
1. **Option #1: (x, y) → (y, -x)**
- If you apply this transformation, for a point (1, 2):
- It transforms to (2, -1). This mapping does not represent a 90-degree counterclockwise rotation.
2. **Option #2: (x, y) → (-y, x)**
- If you apply this transformation, for a point (1, 2):
- It transforms to (-2, 1). This is indeed the correct transformation for a 90-degree counterclockwise rotation.
3. **Option #3: (x, y) → (-x, -y)**
- If you apply this transformation, for a point (1, 2):
- It transforms to (-1, -2). This represents a rotation of 180 degrees and is not what we want.
Based on this analysis, the correct function mapping that corresponds to a 90-degree counterclockwise rotation about the origin is:
**Option #2: (x, y) → (-y, x)**
1. **Option #1: (x, y) → (y, -x)**
- If you apply this transformation, for a point (1, 2):
- It transforms to (2, -1). This mapping does not represent a 90-degree counterclockwise rotation.
2. **Option #2: (x, y) → (-y, x)**
- If you apply this transformation, for a point (1, 2):
- It transforms to (-2, 1). This is indeed the correct transformation for a 90-degree counterclockwise rotation.
3. **Option #3: (x, y) → (-x, -y)**
- If you apply this transformation, for a point (1, 2):
- It transforms to (-1, -2). This represents a rotation of 180 degrees and is not what we want.
Based on this analysis, the correct function mapping that corresponds to a 90-degree counterclockwise rotation about the origin is:
**Option #2: (x, y) → (-y, x)**
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