The points A (7,6) and B (2,1) are 3 units and 2 units respectively from the line L and are on the opposite sides of L. Find the coordinates of the point where the interval AB crosses the line L.
The distance $\displaystyle \overline{AB}$ is divided by the line L into 2 parts with the ratio of 2 : 3 (from B to A)
You find this ratio with the coordinates of the points A and B.
Therefore the coordinates of the point of intersection are $\displaystyle \left(2+\frac25 \cdot (7-5),1+\frac25 \cdot (6-1)\right)$ That means this point has the coordinates (4, 3)
There are 2 lines which satisfy the given conditions.