Question

Find the midpoint of the segment with the following endpoints.
(−3,−8) and (3,−2)

Answer 1

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:

1. For the \(x\)-coordinate:
\[
\frac{-3 + 3}{2} = \frac{0}{2} = 0
\]

2. 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 \((0, -5)\).