Question

Which of the following mapping is used for a 270 degree (counterclockwise) rotation?(1 point)%0D%0AResponses%0D%0A%0D%0A(x, y)→(y, −x)%0D%0A(%0D%0A𝑥%0D%0A,%0D%0A %0D%0A𝑦%0D%0A)%0D%0A→%0D%0A(%0D%0A𝑦%0D%0A,%0D%0A %0D%0A−%0D%0A𝑥%0D%0A)%0D%0A(x, y)→(y, −x)%0D%0A(%0D%0A𝑥%0D%0A,%0D%0A %0D%0A𝑦%0D%0A)%0D%0A→%0D%0A(%0D%0A𝑦%0D%0A,%0D%0A %0D%0A−%0D%0A𝑥%0D%0A)%0D%0A%0D%0A(x, y)→(−y, x)%0D%0A(%0D%0A𝑥%0D%0A,%0D%0A %0D%0A𝑦%0D%0A)%0D%0A→%0D%0A(%0D%0A−%0D%0A𝑦%0D%0A,%0D%0A %0D%0A𝑥%0D%0A)%0D%0A (x, y)→(−y, x)%0D%0A(%0D%0A𝑥%0D%0A,%0D%0A %0D%0A𝑦%0D%0A)%0D%0A→%0D%0A(%0D%0A−%0D%0A𝑦%0D%0A,%0D%0A %0D%0A𝑥%0D%0A)%0D%0A%0D%0A(x, y)→(−y, −x)%0D%0A(%0D%0A𝑥%0D%0A,%0D%0A %0D%0A𝑦%0D%0A)%0D%0A→%0D%0A(%0D%0A−%0D%0A𝑦%0D%0A,%0D%0A %0D%0A−%0D%0A𝑥%0D%0A)%0D%0A (x, y)→(−y, −x)%0D%0A(%0D%0A𝑥%0D%0A,%0D%0A %0D%0A𝑦%0D%0A)%0D%0A→%0D%0A(%0D%0A−%0D%0A𝑦%0D%0A,%0D%0A %0D%0A−%0D%0A𝑥%0D%0A)%0D%0A%0D%0A(x, y)→(−x, −y)

Answer 1

The mapping used for a 270-degree (counterclockwise) rotation can be determined through trigonometric transformations. A 270-degree counterclockwise rotation can also be understood as a 90-degree clockwise rotation.

The transformation for a 90-degree clockwise rotation is given by:
\[
(x, y) \rightarrow (y, -x)
\]
Therefore, for a 270-degree counterclockwise rotation, the correct mapping is:
\[
(x, y) \rightarrow (y, -x)
\]

So the correct response from your list is:
\[
(x, y) \rightarrow (y, -x)
\]