Question

Find the midpoint of the segment with the following endpoints.
(0,3) and (8,−1)

Answer 1

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

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

Given the endpoints \((0, 3)\) and \((8, -1)\):

- Here, \(x_1 = 0\), \(y_1 = 3\), \(x_2 = 8\), and \(y_2 = -1\).

Now, plug these values into the midpoint formula:

\[
\text{Midpoint} = \left( \frac{0 + 8}{2}, \frac{3 + (-1)}{2} \right)
\]

Calculating the \(x\)-coordinate:

\[
\frac{0 + 8}{2} = \frac{8}{2} = 4
\]

Calculating the \(y\)-coordinate:

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

Therefore, the midpoint of the segment is:

\[
\boxed{(4, 1)}
\]