1. The PDF Coordinate Matrix Model
In the PDF ISO 32000-1 specification, text positioning is defined by a 6-element affine transformation matrix:
$$\begin{bmatrix} x' & y' & 1 \end{bmatrix} = \begin{bmatrix} x & y & 1 \end{bmatrix} \begin{bmatrix} a & b & 0 \\ c & d & 0 \\ e & f & 1 \end{bmatrix}$$
Here, [a, b, c, d] control scaling and rotation, while [e, f] define horizontal and vertical translation offsets. Furthermore, PDF coordinates place $(0,0)$ at the bottom-left corner of the page, whereas modern document models (DOM, Markdown AST) place $(0,0)$ at the top-left corner.