Final answer:
The student's work showed a misapplication of the distance formula. The correct method to find the distance between two points on the coordinate plane, in this case between r(-3,-4) and s(5,7), involves the formula d = √((x2 - x1)^2 + (y2 - y1)^2), which equals √185 for these points.
Step-by-step explanation:
The student's question involves finding the distance between two points, r(-3,-4) and s(5,7), on the coordinate plane. However, the work shown in the question reflects a misunderstanding of the formula to compute this distance. The correct formula to determine the distance d between two points (x1, y1) and (x2, y2) is given by d = √((x2 - x1)^2 + (y2 - y1)^2). When we apply this formula to the points (-3,-4) and (5,7), we get d = √((5 - (-3))^2 + (7 - (-4))^2) = √((5 + 3)^2 + (7 + 4)^2) = √(8^2 + 11^2) = √(64 + 121) = √185.