Question
A figure is rotated 90 degrees counterclockwise about the origin. Which of the following function mappings was applied? (1 point)
Responses
(x,y)→(y, x)
(x,y)→(y, x)
(x,y)→(y, −x)
(x,y)→(y, −x)
(x,y)→(-x, y)
(x,y)→(-x, y)
(x,y)→(-y ,x)
Responses
(x,y)→(y, x)
(x,y)→(y, x)
(x,y)→(y, −x)
(x,y)→(y, −x)
(x,y)→(-x, y)
(x,y)→(-x, y)
(x,y)→(-y ,x)
Answers
GPT-4o mini
When a point \((x, y)\) is rotated 90 degrees counterclockwise about the origin, the new coordinates can be expressed with the following mapping:
\[
(x, y) \rightarrow (-y, x)
\]
This means that on rotation, the x-coordinate becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.
Therefore, the correct function mapping for a 90-degree counterclockwise rotation about the origin is:
\[
(x,y) \rightarrow (-y, x)
\]
\[
(x, y) \rightarrow (-y, x)
\]
This means that on rotation, the x-coordinate becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.
Therefore, the correct function mapping for a 90-degree counterclockwise rotation about the origin is:
\[
(x,y) \rightarrow (-y, x)
\]