Final answer:
Option D. After a 90° rotation about the z-axis, each point's coordinates transform as follows: (3,2) to (-2, 3), (2, -3) to (3, 2), (-2,3) to (-3, -2), and (-3,2) to (-2, -3), representing a standard counter-clockwise rotation in the xy-plane.
Step-by-step explanation:
The coordinates of V' after a 90° rotation about the z-axis can be determined by applying the rules for rotation in the coordinate system. Given a point (x, y) in the plane, a 90° rotation about the z-axis (counter-clockwise) will transform this point to (-y, x). Therefore, we can calculate the new coordinates for each given point:
- (3,2) becomes (-2, 3)
- (2, -3) becomes (3, 2)
- (-2,3) becomes (-3, -2)
- (-3,2) becomes (-2, -3)
The new positions correspond to moving horizontally to the left side of the coordinate system and vertically upward in the coordinate system for positive y-values and to the right and downward for negative y-values, respectively.