Question

Find the midpoint of the segment with the following endpoints.
left parenthesis, 5, comma, 7, right parenthesis, and , left parenthesis, minus, 3, comma, 10, right parenthesis
(5,7) and (−3,10)

Answer 1

To find the midpoint of a 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 \((5, 7)\) and \((-3, 10)\), we can identify \(x_1 = 5\), \(y_1 = 7\), \(x_2 = -3\), and \(y_2 = 10\).

Now, plug these values into the formula:

\[
\text{Midpoint} = \left( \frac{5 + (-3)}{2}, \frac{7 + 10}{2} \right)
\]

Calculating each component:

1. For the x-coordinate:
\[
\frac{5 - 3}{2} = \frac{2}{2} = 1
\]

2. For the y-coordinate:
\[
\frac{7 + 10}{2} = \frac{17}{2} = 8.5
\]

Thus, the midpoint of the segment is:

\[
\boxed{(1, 8.5)}
\]