At what coordinate is the D-brane located in the T dual world?

I have a simple question on the geometrical intuition of D branes. I am currently reading the TASI notes by Polchinski.

Say one has a bosonic open string with all Neumann boundary conditions and compactifies $X^{25} sim X^{25} + 2 pi R$. Via T duality, there is a dual "world" with coordinate $X’^{25} sim X’^{25} + frac{2 pi alpha’}{R}$. In the $X’^{25}$ coordinate, the Neumann boundary condition becomes Dirichlet, i.e. $partial_t X’^{25} = 0$. This means that, in the T dual world, our open string is stuck to a D brane in the $X’^{25}$ direction.

My simple question is, what is the position coordinate of this D brane? I.e., if the string’s end point satisfies $partial_t X’^{25} = 0$, then it also satisfies $X’^{25} = x$ for some constant $x$. What determines this $x$?

Because we have $X^{25}$ translational symmetry in the original world, I cannot see what this variable $x$ could even depend on.