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 do we translate it by?

Answer 1

To translate the rectangle in Quadrant III to overlap with the rectangle in Quadrant I, you would need to translate it by the vector that connects the corresponding vertices of the two rectangles. In other words, you would need to translate it by the difference in position of the two corresponding vertices. You can find this vector by subtracting the coordinates of the corresponding vertices of the two rectangles.