To determine the congruency of the rectangle in Quadrant III to the rectangle in Quadrant I after rotating it 90 degrees clockwise about the origin, the next step would be to translate the rotated rectangle to align it with the position of the rectangle in Quadrant I.
To translate the rectangle, you need to identify the coordinates of a corresponding vertex of the rectangle in Quadrant III after the rotation.
Assuming the original rectangle in Quadrant III has its vertices defined by specific coordinates, your translation will typically involve moving its center or a specific vertex to the same position as the corresponding vertex of the rectangle in Quadrant I.
If we denote the translation vector as \((x, y)\), where \(x\) and \(y\) are the differences in the x-coordinates and y-coordinates, respectively, between a vertex of the rotated rectangle and the corresponding vertex of the rectangle in Quadrant I, you can apply this translation to all the vertices of the rotated rectangle.
Thus, the translation you need could be expressed as:
Translate by \((x, y)\)
Where \(x\) and \(y\) are determined based on the coordinates of corresponding vertices of the two rectangles.
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