Question

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

(2,6)
and (7,−10)

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:

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

In this case, the endpoints are \((2, 6)\) and \((7, -10)\).

Substituting the coordinates into the formula:

- \(x_1 = 2\)
- \(y_1 = 6\)
- \(x_2 = 7\)
- \(y_2 = -10\)

Now, plug these values into the formula:

\[
\text{Midpoint} = \left( \frac{2 + 7}{2}, \frac{6 + (-10)}{2} \right)
\]

Calculating the x and y coordinates separately:

1. For the x-coordinate:

\[
\frac{2 + 7}{2} = \frac{9}{2} = 4.5
\]

2. For the y-coordinate:

\[
\frac{6 - 10}{2} = \frac{-4}{2} = -2
\]

Putting it all together, the midpoint of the line segment is:

\[
\left( 4.5, -2 \right)
\]

Thus, the midpoint is \((4.5, -2)\).