Question

Find the midpoint of the segment with the following endpoints.
left parenthesis, 3, comma, 1, right parenthesis, and , left parenthesis, minus, 7, comma, minus, 9, right parenthesis
(3,1) and (−7,−9)

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:

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

For the endpoints \((3, 1)\) and \((-7, -9)\):

- \(x_1 = 3\)
- \(y_1 = 1\)
- \(x_2 = -7\)
- \(y_2 = -9\)

Now plug in the values:

\[
\text{Midpoint} = \left( \frac{3 + (-7)}{2}, \frac{1 + (-9)}{2} \right)
\]

Calculating the x-coordinate of the midpoint:

\[
\frac{3 - 7}{2} = \frac{-4}{2} = -2
\]

Calculating the y-coordinate of the midpoint:

\[
\frac{1 - 9}{2} = \frac{-8}{2} = -4
\]

Therefore, the midpoint of the segment is:

\[
\text{Midpoint} = (-2, -4)
\]