Question

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

Answer 1

To find the midpoint of a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\), we use the midpoint formula:

\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

Given the endpoints \((-2, 3)\) and \((8, -2)\):

- \(x_1 = -2\)
- \(y_1 = 3\)
- \(x_2 = 8\)
- \(y_2 = -2\)

Now, we substitute these values into the formula:

\[
\text{Midpoint} = \left( \frac{-2 + 8}{2}, \frac{3 + (-2)}{2} \right)
\]

Calculating the x-coordinate:

\[
\frac{-2 + 8}{2} = \frac{6}{2} = 3
\]

Calculating the y-coordinate:

\[
\frac{3 + (-2)}{2} = \frac{1}{2} = 0.5
\]

Thus, the midpoint of the segment is

\[
\boxed{(3, 0.5)}
\]