A figure is rotated 90 degrees counterclockwise about the origin. Which of the following function mappings was applied? Enter the number of the correct option.

Question

Option 1: (x, y) -> (y, -x)
Option 2: (x, y) -> (-y, x)
Option 3: (x, y) -> (-x, -y)
Option 4: (x, y) -> (y, x)

The mapping for a 90-degree counterclockwise rotation is option #___.

Answer 1

To determine the function mapping for a 90-degree counterclockwise rotation about the origin, we can analyze how the coordinates of a point \((x, y)\) change.

When a point \((x, y)\) is rotated 90 degrees counterclockwise, it moves to the point \((-y, x)\). Thus, the correct mapping for a 90-degree counterclockwise rotation is:

\[ (x, y) \rightarrow (-y, x) \]

Now, let's review the provided options:

1. Option 1: \((x, y) \rightarrow (y, -x)\)
2. Option 2: \((x, y) \rightarrow (-y, x)\)
3. Option 3: \((x, y) \rightarrow (-x, -y)\)
4. Option 4: \((x, y) \rightarrow (y, x)\)

The correct answer is:

Option 2: (x, y) → (-y, x)

Therefore, the mapping for a 90-degree counterclockwise rotation is option #2.