Final answer:
The correct transformation rule for reflecting a point across the x-axis is that (x, y) changes to (x, -y), meaning that the y-coordinate changes its sign.
Step-by-step explanation:
When reflecting a point across the x-axis, the x-coordinate remains the same, but the y-coordinate changes its sign. So the correct answer to the question of which rule is true when reflecting across the x-axis is that the point (x, y) changes to (x, -y). This means that option B) (x, y) changes to (-x, y) is incorrect because it suggests changing the x-coordinate, and option D) (x, y) changes to (y,x) describes a reflection over the line y=x, not the x-axis. Option C ((-x, -y)) is also incorrect because it implies inverting both coordinates, which would be a reflection over the origin. Therefore, option A) (x, y) changes to (x, y) is the only one that does not change the coordinates appropriately for a reflection over the x-axis.