Final answer:
Rotations of 180 degrees and reflections across a line of symmetry or a diagonal can map a rectangle onto itself.
Step-by-step explanation:
The transformations that can carry a rectangle onto itself include certain rotations and reflections that maintain the figure's congruence and orientation within a plane. Specifically:
B. Rotate by 180 degrees clockwise using center P is a transformation that would carry rectangle ABCD onto itself because a 180-degree rotation will map all corners back onto their original locations.
C. Reflect across line m, assuming line m is an axis of symmetry for the rectangle (for example, a median through the center of the rectangle), this reflection would also map the rectangle onto itself.
D. Reflect across diagonal AC, if AC is a diagonal of the rectangle, then reflecting the rectangle across this diagonal will also map it onto itself, as diagonals of a rectangle are axes of symmetry.
Rotating by 90 degrees (option A) will not map the rectangle onto itself unless ABCD is a square, which is a specific type of rectangle.
Similarly, translating by the directed line segment from A to B (option E) will move the rectangle to a new position, rather than mapping it onto itself.