Question
A figure is rotated 90 degrees counterclockwise about the origin. Which of the following function mappings was applied?
Option 1: (x,y)>(y,-x)
Option 2: (x,y)>(-y,x)
Option 3: (x,y)>(-x,-y)
Option 4: (x,y)>(y,x)
Option 1: (x,y)>(y,-x)
Option 2: (x,y)>(-y,x)
Option 3: (x,y)>(-x,-y)
Option 4: (x,y)>(y,x)
Answers
GPT-4o mini
To determine the correct function mapping for a 90-degree counterclockwise rotation about the origin, we need to apply the transformation to a point \((x, y)\).
A 90-degree counterclockwise rotation of a point \((x, y)\) results in a new point \((-y, x)\).
Now let's analyze the given options:
- **Option 1**: \((x, y) \to (y, -x)\) — This corresponds to a 90-degree clockwise rotation since the \(y\) coordinate becomes the new \(x\) and the negative of the \(x\) coordinate becomes the new \(y\).
- **Option 2**: \((x, y) \to (-y, x)\) — This is the correct transformation for a 90-degree counterclockwise rotation.
- **Option 3**: \((x, y) \to (-x, -y)\) — This transformation reflects the point through the origin (180-degree rotation).
- **Option 4**: \((x, y) \to (y, x)\) — This corresponds to reflecting over the line \(y = x\), which is not a rotation.
Therefore, the correct mapping for a 90-degree counterclockwise rotation about the origin is **Option 2: \((x, y) \to (-y, x)\)**.
A 90-degree counterclockwise rotation of a point \((x, y)\) results in a new point \((-y, x)\).
Now let's analyze the given options:
- **Option 1**: \((x, y) \to (y, -x)\) — This corresponds to a 90-degree clockwise rotation since the \(y\) coordinate becomes the new \(x\) and the negative of the \(x\) coordinate becomes the new \(y\).
- **Option 2**: \((x, y) \to (-y, x)\) — This is the correct transformation for a 90-degree counterclockwise rotation.
- **Option 3**: \((x, y) \to (-x, -y)\) — This transformation reflects the point through the origin (180-degree rotation).
- **Option 4**: \((x, y) \to (y, x)\) — This corresponds to reflecting over the line \(y = x\), which is not a rotation.
Therefore, the correct mapping for a 90-degree counterclockwise rotation about the origin is **Option 2: \((x, y) \to (-y, x)\)**.