Question

Calculate the midpoint of the line segment formed with the endpoints shown.

(2,4) and (5,-1)

Answer 1

To find the midpoint of a line segment formed by the 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 \((2, 4)\) and \((5, -1)\), we can assign:

- \(x_1 = 2\)
- \(y_1 = 4\)
- \(x_2 = 5\)
- \(y_2 = -1\)

Now, plug these values into the midpoint formula:

\[
x\text{-coordinate of midpoint} = \frac{x_1 + x_2}{2} = \frac{2 + 5}{2} = \frac{7}{2} = 3.5
\]

\[
y\text{-coordinate of midpoint} = \frac{y_1 + y_2}{2} = \frac{4 + (-1)}{2} = \frac{4 - 1}{2} = \frac{3}{2} = 1.5
\]

Thus, the midpoint of the line segment with the endpoints \((2, 4)\) and \((5, -1)\) is

\[
\left( 3.5, 1.5 \right)
\]