Minimizing Distance to a Line from Two Points

Given a straight line $l$ and two points $A$ and $B$, consider the following cases:
a) Points $A$ and $B$ lie on opposite sides of the line $l$.
b) Points $A$ and $B$ lie on the same side of the line $l$.
Find a point $X$ on the line $l$ such that the sum of the distances $AX + BX$ is minimised.