6 of 116 of 11 Items Question A figure is rotated 90 degrees counterclockwise about the origin. Which of the following function mappings was applied? (1 point) Responses Option #1: (x,y)→(y,−x) Option #1: (x,y)→(y,−x) Option #2: (x,y)→(−y,x) Option #2: (x,y)→(−y,x) Option #3: (x,y)→(−x,−y) Option #3: (x,y)→(−x,−y) Skip to navigation page 1 of 1

Answer 1

To determine which function mapping corresponds to a 90-degree counterclockwise rotation about the origin, we can analyze the transformations provided.

1. Option #1: (x, y) → (y, -x)

   • If you apply this transformation, for a point (1, 2):
     • It transforms to (2, -1). This mapping does not represent a 90-degree counterclockwise rotation.

2. Option #2: (x, y) → (-y, x)

   • If you apply this transformation, for a point (1, 2):
     • It transforms to (-2, 1). This is indeed the correct transformation for a 90-degree counterclockwise rotation.

3. Option #3: (x, y) → (-x, -y)

   • If you apply this transformation, for a point (1, 2):
     • It transforms to (-1, -2). This represents a rotation of 180 degrees and is not what we want.

Based on this analysis, the correct function mapping that corresponds to a 90-degree counterclockwise rotation about the origin is:

Option #2: (x, y) → (-y, x)