1. The point can be anywhere at all.

2. Yes, this is only in 2-dimensions with variables x and y. Defining "closest" is the main problem I have with this. What would the point have to satisfy for it to be considered the "closest" to a triple intersection?

I have found a few set of points that satisfy different things:

1.

is the point such that it has the minimum squared distances from the point to the y coordinate of the lines (ie, its the point on the line of best fit that has the smallest error).

2.

is the point such that the summed distance (perpendicular distance) from each line to the point is minimised.

3.

is the point such that the summed squared distance (perpendicular distance) from each line to the point is minimised.

4.

is the centre of the triangle formed by the 3 lines.