To determine the midpoint of a line segment with given endpoints [tex]\((-2, -3)\)[/tex] and [tex]\((-11, 20)\)[/tex], we can use the midpoint formula. The midpoint [tex]\(M\)[/tex] of a segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Let's identify our coordinates:
- The first endpoint [tex]\((x_1, y_1)\)[/tex] is [tex]\((-2, -3)\)[/tex].
- The second endpoint [tex]\((x_2, y_2)\)[/tex] is [tex]\((-11, 20)\)[/tex].
Now, substitute these coordinates into the midpoint formula:
First, we find the x-coordinate of the midpoint by averaging the x-coordinates of the endpoints:
[tex]\[
x_{\text{mid}} = \frac{x_1 + x_2}{2} = \frac{-2 + (-11)}{2} = \frac{-2 - 11}{2} = \frac{-13}{2} = -6.5
\][/tex]
Next, we find the y-coordinate of the midpoint by averaging the y-coordinates of the endpoints:
[tex]\[
y_{\text{mid}} = \frac{y_1 + y_2}{2} = \frac{-3 + 20}{2} = \frac{-3 + 20}{2} = \frac{17}{2} = 8.5
\][/tex]
Therefore, the midpoint [tex]\(M\)[/tex] of the segment with endpoints [tex]\((-2, -3)\)[/tex] and [tex]\((-11, 20)\)[/tex] is:
[tex]\[
M = (-6.5, 8.5)
\][/tex]
So, the coordinates of the midpoint are [tex]\((-6.5, 8.5)\)[/tex].
