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

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)

1 answer

To determine the correct function mapping for a 90-degree counterclockwise rotation about the origin, we examine each option:

  • Option #1: (x,y)→(y,−x): This mapping represents a rotation of 90 degrees clockwise.

  • Option #2: (x,y)→(−y,x): This mapping represents a rotation of 90 degrees counterclockwise.

  • Option #3: (x,y)→(−x,−y): This mapping reflects the point across the origin (180-degree rotation).

  • Option #4: (x,y)→(y,x): This mapping reflects the point across the line y = x (which is not a rotation).

Therefore, the correct option for a 90-degree counterclockwise rotation about the origin is:

Option #2: (x,y)→(−y,x).