Question

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.
Option #1: (x,y)→(y,−x) Option #2: (x,y)→(−y,x) Option #3: (x,y)→(−x,−y) Option #4: (x,y)→(y,x)

Answer 1

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

When a point \((x, y)\) is rotated 90 degrees counterclockwise, the new coordinates can be calculated as follows:
- The \(x\) coordinate becomes the negative of the original \(y\) coordinate.
- The \(y\) coordinate becomes the original \(x\) coordinate.

Therefore, the transformation can be represented as:
\[
(x, y) \rightarrow (-y, x)
\]

This corresponds to Option #2:
\[
Option \#2: (x,y) \rightarrow (-y,x)
\]

Thus, the correct option is **2**.