Final answer:
In Mathematics, the transformation given by (x, y) → (-x, y) represents a reflection across the y-axis. Upon reflection, point A with coordinates (Ax, Ay) becomes point A' with coordinates (-Ax, Ay). Therefore, the correct location for point A' will be (-A, B).
Step-by-step explanation:
The subject in question is Mathematics, specifically dealing with transformations in the coordinate plane. The transformation described is a reflection across the y-axis, which can be represented by the transformation rule (x, y) → (-x, y). When point A on triangle ABC is subjected to this transformation, point A's x-coordinate is negated while its y-coordinate remains unchanged.
Let's consider point A to have coordinates (Ax, Ay). After the reflection, point A' will have coordinates (-Ax, Ay). This transformation essentially flips the point over the y-axis to a new position that is the same vertical distance from the y-axis but on the opposite side. Using this information, we can determine that the correct answer for the location of point A' after the reflection is a) A' will be at (-A, B), where A is the x-coordinate and B is the y-coordinate of the original point A.