Interpolating geographic coordinates

Question

I have two geographic coordinates. Let's call them $A$ and $B$:

A = latitude 41.34759, longitude -75.77415

B = latitude 41.34769, longitude -75.77404

My unknown is a third coordinate $C$. $C$ lies between $A$ and $B$. Additionally, I know $C$ is $15$ meters away from $A$.

Is it possible to calculate the coordinates of $C$?

Answer 1

HINT:

First find the distance from A to B in meters in x-direction and y-direction..

Now it's obviously the distance between this point is so small that we can assume that that we are working on 2D plane, rather that on a sphere.

Let A be point at $(0,0)$, then we can find the position of $B$, using the calculation we made earlier. Now using the slope formula find the equation of the line that passes through $A$ and $B$. Then draw a circle, centered on A with radius $r=15m$. The equation for the circle will be:

$$x^2 + y^2 = 15$$

Now find the intersection point the line and the circle, because there are 2 intersection points, exclude the one that's further from $B$.

Now convert back to latitude and longitude.