The point that divides the line segment joining $A(x_1, y_1, z_1)$ and $B(x_2, y_2, z_2)$ internally in the ratio $m : n$ has coordinates:

Internal section formula: when point $P$ divides $\overline{AB}$ such that $AP : PB = m : n$, then $P = \left(\dfrac{m x_2 + n x_1}{m + n}, \dfrac{m y_2 + n y_1}{m + n}, \dfrac{m z_2 + n z_1}{m + n}\right)$. The weight $m$ multiplies the *far* endpoint ($B$) and $n$ multiplies the near endpoint ($A$). Easy to flip the assignment if you don't think about which side the ratio means. When $m = n$, this collapses to the midpoint formula (option C).