2. In the Cartesian coordinate system, a moving line segment $AB$ of length 3 is sliding on the $x$-axis, with point $A$ to the left of point $B$, and $C(4,4), D(0,1)$. Then the minimum perimeter of quadrilateral $ABCD$ is $(\quad)$.
(A) $7+3 \sqrt{3}$
(B) 13
(C) $8+\sqrt{26}$
(D) $8+3 \sqrt{3}$
2. C.

As shown in Figure 2, the point $D$ is symmetric to the $x$-axis at point $D_{1}(0,-1)$. Translating point $D_{1}$ 3 units to the right yields point $D_{2}(3,-1)$. Connecting $C D_{2}$, we find that quadrilateral $A B D_{2} D_{1}$ is a parallelogram,
$$
\begin{array}{l}
B D_{2}=A D_{1}=A D, \\
A D+B C=B D_{2}+B C \geqslant C D_{2}=\sqrt{26} .
\end{array}
$$

Therefore, the minimum perimeter of quadrilateral $A B C D$ is
$$
8+\sqrt{26} .
$$