Spatial Null Model Creation

I have a dataset with a few sites (Lat/Long coordinates). I would like to be able to keep their spatial arrangement (i.e. the direction and distance from each other) and calculate their distance to a shapefile line. Then repeat the process 100 times.

My first stab at this is to create two random variables (random x and random y). Random Y would be added to the original latitude and random X would be added to the original longitude coordinates. Then project the new coordinates and recalculate the value and plot out the observed distribution relative to the null distribution of null model spatial points.

Does anyone have a cleaner or more elegant way of completing this task in R?