Final answer:
Points A', B', and C' rotated 90 degrees become A''(3, 3), B''(2, 0), and C''(-1, 4) respectively, using the 90-degree rotation rules in the Cartesian coordinate system.
Step-by-step explanation:
The student asked about rotating the points A'(-3, 3), B'(0, -2), and C'(4, 1) by 90 degrees. To do this, we apply a rotation matrix to each point or we can use the rule for 90-degree rotation around the origin, which switches the x and y values and changes the sign of the new x-value. For example, rotating A'(-3, 3) 90 degrees results in A''(3, 3) because we switch the x and y and change the sign of the former x to get the new coordinates. We would apply the same rule to B' and C' to get their rotated positions, B''(2, 0) and C''(-1, 4) respectively.