To find the midpoint of a line segment in the [tex]\(xy\)[/tex]-coordinate plane with given endpoints, we use the midpoint formula. The formula for the midpoint [tex]\((x_m, y_m)\)[/tex] of a segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
(x_m, y_m) = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Here, the endpoints are given as [tex]\((-6, 3)\)[/tex] and [tex]\( (4, -5) \)[/tex].
1. To find the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[
x_m = \frac{-6 + 4}{2} = \frac{-2}{2} = -1
\][/tex]
2. To find the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[
y_m = \frac{3 + (-5)}{2} = \frac{3 - 5}{2} = \frac{-2}{2} = -1
\][/tex]
So the midpoint is [tex]\((-1, -1)\)[/tex].
Now, let’s determine the correct answer from the given options:
- A [tex]\((-5, 4)\)[/tex]
- B [tex]\((-2, -2)\)[/tex]
- C [tex]\((-1, -1)\)[/tex]
- D [tex]\((0, -1)\)[/tex]
- E [tex]\((1, -2)\)[/tex]
The calculated midpoint [tex]\((-1, -1)\)[/tex] matches option C.
Thus, the correct option is:
C [tex]\((-1, -1)\)[/tex]
