Final answer:
Rotating a slope triangle 90 degrees around the origin changes the slope to the negative reciprocal of the original slope. The new slope, after rotation, with an original slope of 3, would be -1/3.
Step-by-step explanation:
When you rotate a slope triangle 90 degrees around the origin, the slope of the new slope triangle will be the negative reciprocal of the original slope. Since the original slope is given as 3 (a rise of 3 units for every run of 1 unit), after a 90-degree rotation, the x-component (run) and y-component (rise) of the slope are swapped, and the new slope has a run of -3 and a rise of 1. Therefore, the new slope is -1/3.