To find the coordinates of the other endpoint of a line segment given the midpoint and one endpoint, you can use the midpoint formula. The midpoint formula in a 2D plane is given by:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two endpoints, and the result is the coordinates of the midpoint.
Given:
- Midpoint [tex]\((x_m, y_m) = (11, -5)\)[/tex]
- One endpoint [tex]\((x_1, y_1) = (-4, -8)\)[/tex]
We need to find the coordinates of the other endpoint [tex]\((x_2, y_2)\)[/tex].
We can set up the following equations based on the midpoint formula:
[tex]\[
x_m = \frac{x_1 + x_2}{2} \implies 11 = \frac{-4 + x_2}{2}
\][/tex]
[tex]\[
y_m = \frac{y_1 + y_2}{2} \implies -5 = \frac{-8 + y_2}{2}
\][/tex]
Solve the first equation for [tex]\(x_2\)[/tex]:
[tex]\[
11 = \frac{-4 + x_2}{2}
\][/tex]
[tex]\[
22 = -4 + x_2 \quad \text{(Multiplying both sides by 2)}
\][/tex]
[tex]\[
x_2 = 26
\][/tex]
Solve the second equation for [tex]\(y_2\)[/tex]:
[tex]\[
-5 = \frac{-8 + y_2}{2}
\][/tex]
[tex]\[
-10 = -8 + y_2 \quad \text{(Multiplying both sides by 2)}
\][/tex]
[tex]\[
y_2 = -2
\][/tex]
Therefore, the coordinates of the other endpoint are [tex]\((26, -2)\)[/tex].
So, the correct choice is:
[tex]\[
\boxed{(26, -2)}
\][/tex]
