Question

Find the midpoint of the segment with the following endpoints.
left parenthesis, 9, comma, 8, right parenthesis, and , left parenthesis, 5, comma, 1, right parenthesis
(9,8) and (5,1)

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 \((9, 8)\) and \((5, 1)\), we can identify:

- \(x_1 = 9\)
- \(y_1 = 8\)
- \(x_2 = 5\)
- \(y_2 = 1\)

Now, applying the midpoint formula:

\[
\text{Midpoint} = \left( \frac{9 + 5}{2}, \frac{8 + 1}{2} \right)
\]

Calculating the \(x\)-coordinate:

\[
\frac{9 + 5}{2} = \frac{14}{2} = 7
\]

Calculating the \(y\)-coordinate:

\[
\frac{8 + 1}{2} = \frac{9}{2} = 4.5
\]

Thus, the midpoint of the segment is:

\[
\boxed{(7, 4.5)}
\]