Final answer:
After rotating the point (5, 8) 270 degrees clockwise, the new coordinates of the point would be the (-8, 5).
Step-by-step explanation:
When you rotate a point 270 degrees clockwise around the origin, you are applying a rotation transformation. This transformation can be conducted by rotating the point around the origin.
To find the new coordinates after a rotation, we can use the rules for rotation 270 degrees clockwise, which are the same as the rules for rotation 90 degrees counterclockwise because they are supplementary angles (adding up to 360 degrees). The rule for a 90 degrees counterclockwise rotation (or 270 degrees clockwise rotation) is to switch the x and y coordinates and then change the sign of the new x-coordinate. So, for the point (5, 8), the new y-coordinate would be the original x-coordinate, 5, and the new x-coordinate would be the negative of the original y-coordinate, -8.
Therefore, after a 270 degrees clockwise rotation, the point (5, 8) would be transformed to the point (-8, 5).