Final answer:
The student is looking for the coordinates of point S given T as the midpoint. The midpoint formula is needed to solve for S, but there's a lack of information to provide an exact answer.
Step-by-step explanation:
The student is asking to find the coordinates of point S given that T is the midpoint of the line segment ST and has the coordinates (5, -8). To find the coordinates of point S, we can use the midpoint formula which tells us that the midpoint T is the average of the x-coordinates and y-coordinates of points S and T. If T is the midpoint, then its coordinates are:
(Tx, Ty) = ((Sx + Tx) / 2, (Sy + Ty) / 2)
Since we know T's coordinates are (5, -8), we can set up the equations:
- (5) = (Sx + Tx) / 2
- (-8) = (Sy + Ty) / 2
Which we can solve for Sx and Sy knowing that Tx and Ty are parts of T's coordinates from the question. If we let the coordinates of S be (Sx, Sy), then solving the above system of equations will give us S's coordinates. There seems to be a typo or missing information, because the question indicates a point TR0 and does not provide the coordinates for point T, but based on the context it seems that (5, -8) is meant as point T's coordinates.
Due to the ambiguity in provided information, we are unable to find the precise coordinates for point S without additional information or clarification from the student.