Linear Interpolation

Linear interpolation of straight lines is easy. But you have Lat & Long, which are in degrees, and the lines are not straight, they are on the surface of a sphere. Then you start talking about feet. A change in 1 degree longitude gives you a different number of feet depending how far from the equator you are. This conversion can certainly be done. I would think this type of interpolation would be along a great circle path. Just to give you an idea of what you're getting into, here is a description of a solution to your problem implemented in Java and also in Python.

But first let's understand the problem you are trying to solve. Can you describe a little more what your situation is? We might be able to simplify this, for example, if your points are close together.

Distance between longitudes is non-linear and between latitude is also not exactly same throughout.
Following may help.

Each degree of latitude is approximately 69 miles (111 kilometers) apart. The range varies (due to the earth's slightly ellipsoid shape) from 68.703 miles (110.567 km) at the equator to 69.407 (111.699 km) at the poles.

Unlike latitude, the distance between degrees of longitude varies greatly depending upon your location on the planet. They are farthest apart at the equator and converge at the poles. A degree of longitude is widest at the equator with a distance of 69.172 miles (111.321 kilometers).

Assuming the earth is treated as a sphere, the rigorous solution is to incrementally rotate the starting point about an axis perpendicular to the plane containing the two points and the center of the earth. That is surely a piece of cake for any GIS package. Doing it in Excel would be messy.

I did this decades ago using a book called The American Practical Navigator. What you will find on most posts on this topic is: given two sets of coordinates, compute the great circle distance and angle of departure from the first point.

If I understand your requirement you want to go a certain radial / DME (to use aviation terms) from a starting point or head out on a certain heading for a certain distance and compute the Latitude and Longitude of where you wind up.

This requires working with Napier's Rules for Right Spherical Triangles. Here is one reference: https://www.researchgate.net/publica...Circular_Parts. As I said, I solved this decades ago but alas, the Unix Machine I had it on has long since bit the dust and I would have had to translate it from C.

I suggest you offer a bottle of scotch (or some other incentive) to the local high school trigonometry teacher.

Every 50 feet!? You're going to need some good precision. I do not recommend "leap frogging" - that is move 50 from the start to point A then move 50 feet from point A to point B ... Instead calculate point A as 50 feet from the origin, calculate point B as 100 feet from the origin and so on.

A thought occurred to me, What is the scope of this exercise? Why the 50 feet? What total distances are we talking about?

If it's relatively short distances, then some approximations could be made. A degree of longitude is equal to the cosine of the latitude (1 degree at the equator, .7 degrees at 30 degrees N/S, .5 at 60 degrees N/S and zero at the pole).

For very short distances, you could consider the earth to be flat and use Euclidean Geometry, making the adjustments for the latitude.