I know this shouldn't be too difficult, but, unfortunately, I have forgotten a lot.
Have 2 known points, the distance between those 2 points, and the distance of the line I would like to know the end point of. That is, I want to project past the known end point the differential distance and determine this point.
For example, I have (665306, 1520215), (665578 1520167), and desired distance ~372. The distance between the two points is ~276.
How would I extend past (665578 1520167) 96 = 372 - 276 on the same path and determine that point?
I was looking at projections but this was reliant on a second vector that will allow us to project from vector 2 to vector 1 a perpendicular vector.
I'll label the point $(655306, 1520215)$ as $A$ and the other as $B$. We want to find the point $C$ on the line $AB$ such that $AC = 372$ and $BC = 96$. To do this, we first find the vector $AB$ by subtracting the two points, and then multiply the vector $AB$ by $\frac{372}{276}$. This gives us vector $AC$, and we now add this back to $A$ to find $C$.