Question

which shows the image of rectangle abcd after the rotation (x, y) → (-y, x)?

Explanation:

Step1: Recall rotation rule

The rule $(x,y)\to(-y,x)$ represents a 90 - degree counter - clockwise rotation about the origin.

Step2: Apply rule to rectangle vertices

For a rectangle with vertices, when we apply the rule to each vertex, the orientation of the rectangle will change in a 90 - degree counter - clockwise manner.

Step3: Analyze options

Check each option to see which one has the rectangle rotated 90 degrees counter - clockwise. The rectangle will change from a vertical or horizontal orientation to the opposite.

Answer:

The option where the rectangle is rotated 90 degrees counter - clockwise about the origin. Without specific labels for each option, we can't give a letter - based answer, but the correct one will have the rectangle oriented 90 degrees counter - clockwise compared to the original rectangle ABCD.