Final answer:
The set of reflections that would carry rectangle ABCD onto itself is two reflections over the diagonals, as they are symmetrical and bisect each other, thus bringing the rectangle back to its original position when reflected successively. Given these considerations, the correct answer to the question is option (a): Two reflections over the diagonals would carry rectangle ABCD onto itself.
Step-by-step explanation:
The question asks, Which set of reflections would carry rectangle ABCD onto itself? When considering reflections over different axes or lines, the goal is to determine which reflections would result in the rectangle being mapped onto itself without any changes in orientation or position. Reflections over various lines and axes have different effects on a shape:
- Reflection over the diagonals of a rectangle would indeed map the rectangle onto itself, exchanging corresponding corners. Since a rectangle's diagonals are symmetrical and bisect each other, reflecting over one diagonal and then the other would bring the rectangle back to its original position.
- Reflection over a horizontal axis that passes through the center of the rectangle would map top to bottom and vice versa.
- Reflection over a vertical axis that passes through the center of the rectangle would map left to right and vice versa.
- Reflection over the sides of the rectangle would not generally map the rectangle onto itself unless the reflections happen over lines that coincide with the sides' midpoints.
Given these considerations, the correct answer to the question is option (a): Two reflections over the diagonals would carry rectangle ABCD onto itself.