The first step to determine that the rectangle in Quadrant III is congruent to the rectangle in Quadrant I was to rotate the first rectangle 90 degrees clockwise about the origin. The next step is translating it, but what coordinates do we translate it by?
To translate the rectangle in Quadrant III to overlap with the rectangle in Quadrant I, we need to move it to the right by the distance between the two rectangles. Since the rectangles are congruent, the distance between their centers must be the same as the distance between two corresponding vertices.
To find this distance, you can calculate the difference in the x-coordinates of the two rectangles' centers and use this value as the translation distance.