The canonical way of doing things:
- Figure out how to calculate distances with longitutdes/latitudes. A quick Google search, for example, brings up this.
- Iterate over all points
p_i
and calculate the distanced_i
to the center point. - The point
p_k
withd_k = max_j d_j
will be the point you are looking for.
For distance calculation keep in mind that you can save yourself any operation that won't change the information "further away than", i.e. in euclidic coordinates you could save yourself taking the square root. Also multiplications by any constant can be omitted for this (as long as you don't need to actually know the distance, but only the information which point is the furthest away).