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

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)

(1 point)
Responses

Option #1

Option #2

Option #3

Option #4

Answer 1

When a figure is rotated 90 degrees counterclockwise about the origin, the transformation of the coordinates (x, y) can be described by the mapping:

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

This means the x-coordinate becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.

Thus, the correct answer is Option #2: (x,y) --> (-y,x).