Final answer:
After rotating a rectangle 90 degrees clockwise about the origin, the point J with coordinates (x, y) would have its coordinates changed to (y, -x) to become J'.
Step-by-step explanation:
When a geometrical figure is rotated clockwise 90 degrees about the origin, the coordinates of each point of the figure change according to a specific rule. To find the coordinates of J' after the rotation, if the original coordinates of point J are (x, y), the new coordinates of J' will be (y, -x). This rule is derived from rotating the point around the origin on the Cartesian plane. The point initially at (x, y) will move to a new position where its x-coordinate becomes the opposite of the original y-coordinate, and its y-coordinate becomes the original x-coordinate. As an example, if J were at (3, 4), after the rotation, J' would be at (4, -3).