$25 \cdot 8$ When a sheet of coordinate paper is folded once, $(0,2)$ overlaps with $(4,0)$. If $(7,3)$ overlaps with $(m, n)$, then $m+n$ equals
(A)6.7.
(B) 6.8 .
(C) 6.9 .
(D) 7.0 .
(E)8.0.
(49th American High School Mathematics Examination, 1998)
[Solution] Given $A(0,2)$ and $B(4,0)$, the equation of the axis of symmetry passes through the point $(2,1)$ and is perpendicular to the direction of $k_{A B}=\frac{2-0}{0-4}=-\frac{1}{2}$. Therefore, its equation is
$y-1=2(x-2)$, which simplifies to $y-2 x+3=0$.
Also, $(7,3)$ and $(m, n)$ coincide after folding (along the axis of symmetry). Clearly,
(1) $\left(\frac{7+m}{2}, \frac{3+n}{2}\right)$ lies on the line;
(2) $\frac{n-3}{m-7}$ is parallel to the direction of $k_{A B}=-\frac{1}{2}$. Thus, we have
$$
\left\{\begin{array}{l}
\frac{3+n}{2}-(7+m)+3=0 \\
\frac{n-3}{m-7}=-\frac{1}{2} .
\end{array}\right.
$$

Solving these equations gives $m=0.6, n=6.2$, so $m+n=6.8$. Therefore, the answer is $(B)$.