Final answer:
To determine the new coordinates after a 270-degree clockwise rotation, use the transformation rule x' = y and y' = -x. Substitute the original coordinates of A, B, and C into these equations to find A', B', and C'. This visualizes as flipping over the y-axis and then rotating 180 degrees.
Step-by-step explanation:
The question is asking for the new coordinates of points A', B', and C' after a 270-degree clockwise rotation of triangle ABC around the origin. When rotating a point 270 degrees clockwise, the transformation rule can be found by using the standard rotation formulas with θ = 270 degrees, which results in the transformation equations x' = y and y' = -x.
To find the new coordinates for each point after the rotation, you would substitute the original x and y values of point A into the transformation equations to obtain A'. Repeat this process for points B and C to find B' and C'. For instance, if A has coordinates (x,y), then A' will have coordinates (y, -x) after the rotation.
This rotation can be visualized as flipping the point over the y-axis to its mirror image and then rotating 180 degrees around the origin.