Question

I am trying to calculate point on a line.
I got the points of the edges and one distance between one edge to the point I want to find (which is B).

A(2,4)
B(x,y)
C(4,32)

The distance between A to B is 5.

How can I calculate Bx and By? using the following equations:

d = Math.Sqr((Bx-Ax)^2 + (By-Ay)^2)
d = Math.Sqr((Cx-Bx)^2 + (Cy-By)^2)

and than compare the equations above.

Here is the equations with the points placed:

5 = Math.Sqr((Bx-2)^2 + (By-4)^2)
23.0713366 = Math.Sqr((4-Bx)^2 + (32-By)^2)

or

Math.Sqr((Bx-2)^2 + (By-4)^2) - 5 = Math.Sqr((4-Bx)^2 + (32-By)^2) - 23.0713377

How can I solve this using VBA?

Thank you!

Answer 1

I won’t solve your equations above because they are an unnecessarily complex way to state the problem (and the existence of a solution is questionable in the presence of rounding), but all the points on the line A=(Ax,Ay) to C=(Cx,Cy) can be described as B=(Ax,Ay) + t*(Cx-Ax,Cy-Ay) with t between 0 and 1.

The distance between B and A is then given by d=t*Sqrt((Cx-Ax)^2+(Cy-Ay)^2), which you can invert to get the proper t for a given d – t=d/Sqrt((Cx-Ax)^2+(Cy-Ay)^2)

In your case, B(t) = (2,4) + t*(2,28), t=5/Sqrt(2^2+28^2) ~ 0.178 -> B ~ (2,4) + 0.178 * (2,28) ~ (2.356, 8.987).