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 to rectangle vertices

Take a vertex of rectangle ABCD, say A. If its original coordinates are $(x_1,y_1)$, after rotation its new coordinates will be $(-y_1,x_1)$. When we rotate a rectangle 90 - degree counter - clockwise about the origin, the vertical sides of the original rectangle become horizontal and vice - versa.

Step3: Analyze options

Check each option to see which one has the rectangle in the correct position after a 90 - degree counter - clockwise rotation. The rectangle should be rotated such that what was the top - bottom orientation becomes left - right orientation.

Answer:

The option where the rectangle is rotated 90 degrees counter - clockwise about the origin (the one where the vertical rectangle becomes a horizontal rectangle in the correct orientation). Without specific labels for each option, it's not possible to give a lettered answer, but visually select the one that has the rectangle rotated 90 degrees counter - clockwise.