1. **State the problem:** Find the midpoint of the line segment joining points $A(2,3)$ and $B(4,9)$.\n\n2. **Formula:** The midpoint $M$ of two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is given by:\n$$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$\n\n3. **Apply the formula:** Substitute $x_1=2$, $y_1=3$, $x_2=4$, and $y_2=9$:\n$$M = \left( \frac{2 + 4}{2}, \frac{3 + 9}{2} \right)$$\n\n4. **Simplify:**\n$$M = \left( \frac{6}{2}, \frac{12}{2} \right) = (3, 6)$$\n\n5. **Conclusion:** The midpoint of points $A(2,3)$ and $B(4,9)$ is $\boxed{(3,6)}$.