Final answer:
The sum of the y-coordinates of B'E'A'R'S' after transformation by (x, y) → (x + 6, y + 8) would increase by 40 units from the original sum since each y-coordinate increases by 8 and there are five vertices in a pentagon. Given the options, there is no match, suggesting additional context may be necessary.
Step-by-step explanation:
When transforming the pentagon according to the given rule (x, y) → (x + 6, y + 8), each of the y-coordinates of the vertices of the pentagon will increase by 8. To find the sum of the y-coordinates of the points B'E'A'R'S' after the transformation, it is assumed that there are five vertices (since it's a pentagon), and each of the original y-coordinates would have been increased by 8. Therefore, the sum of the y-coordinates after the transformation is the sum of the original y-coordinates plus 5 times 8, which is an increase of 40 units to the original sum. Without knowing the original y-coordinates, we cannot determine the exact sum after transformation, but we know that it will be the original sum plus 40. However, if we are to assume that the question meant to inquire about the sum of the increments, then the sum would only be the total contribution from the translation, which is simply 5 vertices times the 8-unit increase, equaling 40. As none of the given options (A, B, C, and D) match this result, it appears there may be additional context required to properly answer the question.