Lời giải:

\( I \left\{ \begin{aligned} & x = \frac{x_1 + x_2}{2} = \frac{m - 3}{2} \\ & y = -x + m = \frac{3 - m}{2} + m = \frac{3 + m}{2} \end{aligned} \right. \in \Delta: y=2x+1\)

\(\frac{3 + m}{2} = m - 3 + 1 = m - 2 \)

\(  \Leftrightarrow  3 + m = 2m - 4  \Leftrightarrow  m = 7\)

Vậy chọn \(\boxed{A}\).