To find the coordinates of point B, we can use the midpoint formula. The midpoint formula is given by:
Midpoint = (x1 + x2)/2, (y1 + y2)/2
In this case, we are given that the midpoint of AB is (3,-5). We can substitute this into the midpoint formula to find the coordinates of point B.
Midpoint = (x1 + x2)/2, (y1 + y2)/2
= (3 - x1)/2, (-5 - y1)/2
We can then solve for x1 and y1, which are the coordinates of point A.
x1 = 23 - x2
y1 = 2(-5) - y2
Substituting the given coordinates of the midpoint into these equations, we get:
x1 = 6 - x2
y1 = -10 - y2
We are given that the coordinates of point A are (4,-8). Substituting these values into the equations above, we can solve for x2 and y2, which are the coordinates of point B:
x1 = 6 - x2
4 = 6 - x2
x2 = 2
y1 = -10 - y2
-8 = -10 - y2
y2 = -6
Therefore, the coordinates of point B are (2,-6). This means that the correct answer is option (a), A(4,-8).