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

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)

Answer 1

To determine the function mapping that corresponds to rotating a point \((x, y)\) 90 degrees counterclockwise about the origin, let's analyze how the coordinates change during this transformation.

When a point \((x, y)\) is rotated 90 degrees counterclockwise:

• The x-coordinate becomes the negative of the original y-coordinate.
• The y-coordinate becomes the original x-coordinate.

Thus, the point \((x, y)\) transforms to \((-y, x)\).

Looking at the options provided:

1. Option #1: \((x,y) → (y, -x)\)
2. Option #2: \((x,y) → (-y, x)\)
3. Option #3: \((x,y) → (-x, -y)\)
4. Option #4: \((x,y) → (y, x)\)

The correct mapping for a 90 degrees counterclockwise rotation is Option #2: \((x, y) → (-y, x)\).

So the answer is 2.