Question

Find the midpoint of the segment with the following endpoints.
left parenthesis, minus, 7, comma, 9, right parenthesis, and , left parenthesis, minus, 4, comma, 6, right parenthesis
(−7,9) and (−4,6)

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 \((-7, 9)\) and \((-4, 6)\):

- \(x_1 = -7\), \(y_1 = 9\)
- \(x_2 = -4\), \(y_2 = 6\)

Now, plug these values into the formula:

\[
\text{Midpoint} = \left(\frac{-7 + (-4)}{2}, \frac{9 + 6}{2}\right)
\]

Calculating the x-coordinate:

\[
\frac{-7 - 4}{2} = \frac{-11}{2} = -5.5
\]

Calculating the y-coordinate:

\[
\frac{9 + 6}{2} = \frac{15}{2} = 7.5
\]

Thus, the midpoint of the segment is:

\[
\left(-5.5, 7.5\right)
\]

So the midpoint is \(\boxed{\left(-5.5, 7.5\right)}\).