Question

Find the midpoint of the segment with the following endpoints.
(−9,−10) and (−3,−4)

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:

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

Here, the endpoints are \((-9, -10)\) and \((-3, -4)\). Thus, we can identify:
- \(x_1 = -9\)
- \(y_1 = -10\)
- \(x_2 = -3\)
- \(y_2 = -4\)

Now, we can substitute these values into the midpoint formula.

1. Calculate the x-coordinate of the midpoint:
\[
\frac{x_1 + x_2}{2} = \frac{-9 + (-3)}{2} = \frac{-9 - 3}{2} = \frac{-12}{2} = -6
\]

2. Calculate the y-coordinate of the midpoint:
\[
\frac{y_1 + y_2}{2} = \frac{-10 + (-4)}{2} = \frac{-10 - 4}{2} = \frac{-14}{2} = -7
\]

Combining both coordinates, the midpoint is:
\[
\text{Midpoint} = (-6, -7)
\]

Thus, the midpoint of the segment with endpoints \((-9, -10)\) and \((-3, -4)\) is \(\boxed{(-6, -7)}\).