The distance from a point to a line is given by the projection of a line from the point to some point on the line onto a unit vector orthogonal to the line.

First we need same data.

```
lines = Partition(RandomReal({-1, 1}, {6, 2}), 2)
point = RandomReal({-1, 1}, 2)
Graphics({Line(lines), PointSize(0.02), Red, Point(point)},
Axes -> True)
```

Then we need unit vectors orthogonal to our lines:

```
ortho = Normalize /@ (Subtract @@@ dat).{{0, 1}, {-1, 0}};
```

The distance from the point to the lines is now given by the absolute value of the projection of the line from `point`

to the start of the lines onto the orthogonal unit vector:

```
dist = MapThread((Abs((point - #1).#2)) &, {lines((All, 1)), ortho})
(*{0.0292868, 0.260295, 0.347937}*)
```

It is obvious, for our example, that the first line is closest to the point.