To find the midpoint of a segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\), you can use the midpoint formula:
\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Given the endpoints \((4, 6)\) and \((7, 2)\), we have:
- \(x_1 = 4\)
- \(y_1 = 6\)
- \(x_2 = 7\)
- \(y_2 = 2\)
Now we can substitute these values into the formula:
\[ \text{Midpoint} = \left( \frac{4 + 7}{2}, \frac{6 + 2}{2} \right) \]
Calculating the x-coordinate:
\[ \frac{4 + 7}{2} = \frac{11}{2} = 5.5 \]
Calculating the y-coordinate:
\[ \frac{6 + 2}{2} = \frac{8}{2} = 4 \]
Therefore, the midpoint of the segment is:
\[ \left( 5.5, 4 \right) \]