Final answer:
The question entails translating a point by adding 4 to the x-coordinate and subtracting 1 from the y-coordinate, then reflecting it over the x-axis. However, following these steps for point A (-4, 6) yields a point (0, -5), which does not match any of the provided answer choices.
Step-by-step explanation:
The question involves performing two operations on a point in the coordinate system: a translation and a reflection. First, we apply the translation to the point (x, y), meaning we add 4 to the x-coordinate and subtract 1 from the y-coordinate. After this translation, the coordinates of the point would be (x + 4, y - 1).
For example, if we start with the point A. (-4, 6), after translation, the coordinates would become (-4 + 4, 6 - 1), which simplifies to (0, 5).
The next step is to reflect this translated point over the x-axis. A reflection over the x-axis changes the sign of the y-coordinate but leaves the x-coordinate unchanged. Thus, the reflected point would have coordinates (0, -5).
Unfortunately, none of the given answer choices match the results of the described operations on Point A, which suggests that there may have been a misunderstanding in the instructions or the options provided in the question.