Use the image to answer the question. 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? And what do I translate it by?

Answer 1

To determine that the rectangle in Quadrant III is congruent 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 the correct position in Quadrant I.

To do this, you'll need to translate the rotated rectangle by the appropriate amount to align it with the original rectangle in Quadrant I.

Typically, if the original rectangle in Quadrant I has its bottom-left corner at (x_1, y_1) and the rectangle in Quadrant III has its bottom-left corner at (x_2, y_2), your translation vector will be the difference between these two corner coordinates after rotation.

Thus, if after rotation the coordinates of the rectangle in Quadrant III become (x', y') (based on the original coordinates), you would translate by the vector:

Translation Vector = (x_1 - x', y_1 - y')

You'll add this vector to the coordinates of the rotated rectangle to move it to the same position as the rectangle in Quadrant I.

So, the specific translation you apply would depend on the exact coordinates of the rectangles before and after rotation.