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. The next step is translating it, but what coordinates do we translate it by? (The current coordinates are -1,-4 -5,-4 -1,-6 and -5,-6)

Answer 1

To translate the rectangle in Quadrant III to make it congruent to the rectangle in Quadrant I, we need to translate it horizontally by 6 units and vertically by 6 units.

So, the new coordinates after translation will be:
(-1+6, -4+6) = (5, 2)
(-5+6, -4+6) = (1, 2)
(-1+6, -6+6) = (5, 0)
(-5+6, -6+6) = (1, 0)

Therefore, the new coordinates of the rectangle in Quadrant III after the translation will be (5,2) (1,2) (5,0) and (1,0).