# Find distance of a point relative to a line in geographic coordinates

Suppose there is a spherical rectangle for which I have the lat, long coordinates for each corner. Additionally this rectangle has a center line for which I know the lat, long coordinates of the start, mid and end point (see image below) If you're given a lat, long of a new point (orange circle) is it possible to find the lat, long of the orthogonal intersection with the center line? I know this is pretty easy using cartesian coordinates. But I'd prefer to stick with geographic coordinates since I need to get a very precise distance measurement.

EDIT: So far the only idea I have is to make a grid referenced to the edges and interpolate between them. I plotted the result and it's a little bit off. I'm using the answer from this question

• If it's a rectangle with geographic coordinate reference units, it's not a rectangle, it's a spherical (or spheroidal) rectangle. Please edit the question to provide the GIS software you are using to solve the problem and your best effort to solve it. May 1, 2017 at 18:51