Consider a transformation $T: \mathbb{R}^2 \to \mathbb{R}^2$ that maps the unit basis vectors $\mathbf{i} = (1, 0)$ to $(3, 1)$ and $\mathbf{j} = (0, 1)$ to $(1, 3)$. Which of the following describes the effect of this transformation on the distance between any two arbitrary points $P_1$ and $P_2$?