Final answer:
The reflection over the y-axis changes the x-coordinate of the point (5,-1) to its negative, resulting in (-5,-1), but without the specific translation T, we cannot determine the final coordinates.
Step-by-step explanation:
The rule Ry-axis · T indicates a composition of a reflection over the y-axis followed by a translation T of a point. To find where the point (5,-1) will be after this transformation, we first reflect it over the y-axis. The reflection will change the x-coordinate of the point to its negative value while keeping the y-coordinate the same, resulting in the point (-5,-1). The translation T is not specified in the question, so we cannot determine its effect on the reflected point. Thus, without knowing the specific translation, we cannot identify the final position of the point and select the correct option among a) (6, 0), b) (5, 1), c) (4, -1), or d) (5, -2). Therefore, we cannot confidently provide an answer to this part of the question.