Question

A coordinate plane showing three shaded rectangles.
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. What is the next step?

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Answer 1

I don't have the diagram, so I can't give the specific numbers. Could you upload the figure or give coordinates of one vertex from the rotated rectangle and the corresponding vertex of the Quadrant I rectangle?

In general the next step is a translation. To find the translation vector (h,k) take any vertex of the rotated rectangle (x_r,y_r) and the matching vertex of the Quadrant I rectangle (x_QI,y_QI) and compute
(h,k) = (x_QI − x_r, y_QI − y_r).
Translating the rotated rectangle by (h,k) will place it on the Quadrant I rectangle, proving congruence.