To find the midpoint of the line segment [tex]\(\overline{AB}\)[/tex] where [tex]\(A\)[/tex] has coordinates [tex]\((-1, -1)\)[/tex] and [tex]\(B\)[/tex] has coordinates [tex]\((3, -3)\)[/tex], you can use the midpoint formula. The midpoint [tex]\(M\)[/tex] of a line segment joining two points [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]
Given the points [tex]\(A(-1, -1)\)[/tex] and [tex]\(B(3, -3)\)[/tex]:
1. First, identify the coordinates of points [tex]\(A\)[/tex] and [tex]\(B\)[/tex].
- [tex]\(A: (x_1, y_1) = (-1, -1)\)[/tex]
- [tex]\(B: (x_2, y_2) = (3, -3)\)[/tex]
2. Use the midpoint formula to find [tex]\(M\)[/tex].
[tex]\[ M_x = \frac{x_1 + x_2}{2} = \frac{-1 + 3}{2} = \frac{2}{2} = 1.0 \][/tex]
[tex]\[ M_y = \frac{y_1 + y_2}{2} = \frac{-1 + (-3)}{2} = \frac{-4}{2} = -2.0 \][/tex]
3. Therefore, the coordinates of the midpoint [tex]\(M\)[/tex] are [tex]\((1.0, -2.0)\)[/tex].
Thus, the midpoint of [tex]\(\overline{AB}\)[/tex] is [tex]\((1.0, -2.0)\)[/tex].
