Final answer:
The line segment xy with endpoints x(3, 1) and y(2, -2) is rotated 90 degrees in a counterclockwise direction around the point (2.5, -0.5).
Step-by-step explanation:
To describe the rotation of the line segment xy with endpoints x(3, 1) and y(2, -2) to x²(-3, -1) and y²(-2, 2), we need to find the angle of rotation and the center of rotation. The angle of rotation can be found using the slope formula, and the center of rotation can be found using the midpoint formula.
The slope of line xy is (y2 - y1) / (x2 - x1) = (-2 - 1) / (2 - 3) = -3. The slope of line x²y² is (2 - (-1)) / (-2 - (-3)) = 3.
Since the slopes are negatives of each other, the lines are perpendicular. Therefore, the angle of rotation is 90 degrees. The midpoint of line xy is ((3 + 2) / 2, (1 + (-2)) / 2) = (2.5, -0.5). Therefore, the center of rotation is (2.5, -0.5).