To find the midpoint of a line segment given the endpoints \((x_1, y_1)\) and \((x_2, y_2)\), we can use the midpoint formula:
\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Given the endpoints \((-3, -8)\) and \((3, -2)\), we can assign:
- \(x_1 = -3\)
- \(y_1 = -8\)
- \(x_2 = 3\)
- \(y_2 = -2\)
Now, we can substitute these values into the midpoint formula:
\[ \text{Midpoint} = \left( \frac{-3 + 3}{2}, \frac{-8 + (-2)}{2} \right) \]
Calculating each component:
-
For the \(x\)-coordinate: \[ \frac{-3 + 3}{2} = \frac{0}{2} = 0 \]
-
For the \(y\)-coordinate: \[ \frac{-8 - 2}{2} = \frac{-10}{2} = -5 \]
Putting it all together, the midpoint is:
\[ \text{Midpoint} = (0, -5) \]
Thus, the midpoint of the segment with endpoints \((-3, -8)\) and \((3, -2)\) is \((0, -5)\).