Question

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

a. (x,y) -> (-y,-x)
b. (x,y) -> (y,-x)
c. (x,y) -> (y, x)
d. (x,y) -> (-x,-y)

Answer 1

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

When a point \((x, y)\) is rotated 90 degrees counterclockwise about the origin, the new coordinates can be derived as follows:

1. The x-coordinate of the original point becomes the negative of the y-coordinate.
2. The y-coordinate of the original point becomes the x-coordinate.

Thus, the new coordinates after the 90-degree counterclockwise rotation will be:

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

Comparing this with the provided options:

a. \((x, y) \to (-y, -x)\)
b. \((x, y) \to (y, -x)\)
c. \((x, y) \to (y, x)\)
d. \((x, y) \to (-x, -y)\)

None of the options directly match the correct transformation. However, notice that if we look closely, the function that corresponds to the 90-degree counterclockwise rotation around the origin is actually \((x, y) \to (-y, x)\), but this option isn't among the choices given.

If you are looking for the closest correct answer, then keep in mind:
- The answer that corresponds to a 90-degree clockwise rotation would actually be \((x, y) \to (y, -x)\), which is option b; however, it is not what the question asked for.

To summarize, while none of the provided express the 90-degree counterclockwise rotation correctly, the mapping for \(90^\circ\) counterclockwise is indeed \((x, y) \to (-y, x)\). Hence, based on the given options, none are correct for a 90 degrees counterclockwise rotation.