Given a segment defined by the endpoints A(x1,y1) and B(x2,y2), the coordinates of the midpoint from A to B is given by (xm,ym):
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2} \\ y_m=\frac{y_1+y_2}{2} \end{gathered}[/tex]We are given the coordinates of the midpoint (xm,ym)=(-6,-16), and the coordinates of one of the endpoints, say A=(3,3).
We need to find the coordinates of B(x2,y2). Solving the first equation for x2:
[tex]x_2=2x_m-x_1[/tex]Substituting:
[tex]x_2=2\cdot(-6)-3=-12-3=-15[/tex]Solving the second equation for y2:
[tex]y_2=2y_m-y_1=2\cdot(-16)-3=-32-3=-35[/tex]Thus, the coordinates of the other endpoint are:
B(-15,-35)
