To determine the series of transformations that move a rectangle from Quadrant IV to Quadrant II while showing that the rectangles are congruent, we can analyze the position of the rectangles.
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Reflection: First, we can reflect the rectangle over the y-axis. This transformation will move the rectangle from Quadrant IV to Quadrant III since the points of the rectangle will now have negative x-coordinates.
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Translation: Next, we can translate the rectangle vertically upwards to move it from Quadrant III to Quadrant II.
So, the transformation sequence is reflection, then translation.
Thus, the best description is: reflection, then translation.