1. Given that the point $(x, y)$ moves on the line $x+2 y=3$. When $2^{x}+4^{y}$ takes the minimum value, the distance from the point $(x, y)$ to the origin is ( ).
(A) $\frac{3 \sqrt{5}}{4}$
(B) $\frac{45}{16}$
(C) $\frac{3 \sqrt{2}}{4}$
(D) $\frac{9}{8}$
$$
\begin{array}{l}
-1 . \text { A. } \\
2^{x}+4^{y} \geqslant 2 \sqrt{2^{x+2 y}}=4 \sqrt{2} .
\end{array}
$$

When $x=\frac{3}{2}, y=\frac{3}{4}$, the above expression achieves its minimum value.