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)right arrow (-y, x) Option #2:(x, y)→ (y, -x) Option #2:(x, y)right arrow (y, -x) Option #3:(x, y)→ (y, x) Option #3:(x, y)right arrow (y, x) Option #4:(x, y)→ (-x, -y)
Answers
GPT-4o mini
To determine the correct function mapping for a rotation of 90 degrees counterclockwise about the origin, we can utilize the properties of rotation in the Cartesian coordinate plane.
When a point \((x, y)\) is rotated 90 degrees counterclockwise about the origin, its new coordinates become \((-y, x)\).
Let's analyze the provided options:
- **Option #1:** \((x, y) \rightarrow (-y, x)\)
- **Option #2:** \((x, y) \rightarrow (y, -x)\)
- **Option #3:** \((x, y) \rightarrow (y, x)\)
- **Option #4:** \((x, y) \rightarrow (-x, -y)\)
The correct mapping for a 90-degree counterclockwise rotation is:
**Option #1:** \((x, y) \rightarrow (-y, x)\)
Thus, the answer is **Option #1.**
When a point \((x, y)\) is rotated 90 degrees counterclockwise about the origin, its new coordinates become \((-y, x)\).
Let's analyze the provided options:
- **Option #1:** \((x, y) \rightarrow (-y, x)\)
- **Option #2:** \((x, y) \rightarrow (y, -x)\)
- **Option #3:** \((x, y) \rightarrow (y, x)\)
- **Option #4:** \((x, y) \rightarrow (-x, -y)\)
The correct mapping for a 90-degree counterclockwise rotation is:
**Option #1:** \((x, y) \rightarrow (-y, x)\)
Thus, the answer is **Option #1.**