To find the midpoint of a segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\), you can use the midpoint formula:
\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
For the given points \((10, 4)\) and \((4, 10)\):
- \(x_1 = 10\), \(y_1 = 4\)
- \(x_2 = 4\), \(y_2 = 10\)
Now, substitute these values into the midpoint formula:
\[ \text{Midpoint} = \left( \frac{10 + 4}{2}, \frac{4 + 10}{2} \right) \]
Calculating the x-coordinate:
\[ \frac{10 + 4}{2} = \frac{14}{2} = 7 \]
Calculating the y-coordinate:
\[ \frac{4 + 10}{2} = \frac{14}{2} = 7 \]
Thus, the midpoint is:
\[ \boxed{(7, 7)} \]