To find the midpoint of a line segment given the endpoints [tex]\((-4, -3)\)[/tex] and [tex]\( (7, -5) \)[/tex], we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint [tex]\(M\)[/tex] of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are given by:
[tex]\[ M \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Let's apply the formula step-by-step:
1. Identify the coordinates of the endpoints.
- The coordinates of the first endpoint [tex]\((x_1, y_1)\)[/tex] are [tex]\((-4, -3)\)[/tex].
- The coordinates of the second endpoint [tex]\((x_2, y_2)\)[/tex] are [tex]\((7, -5)\)[/tex].
2. Calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[
\text{x-coordinate} = \frac{x_1 + x_2}{2} = \frac{-4 + 7}{2} = \frac{3}{2} = 1.5
\][/tex]
3. Calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[
\text{y-coordinate} = \frac{y_1 + y_2}{2} = \frac{-3 + (-5)}{2} = \frac{-3 - 5}{2} = \frac{-8}{2} = -4
\][/tex]
Putting these two coordinates together, the coordinates of the midpoint are [tex]\( (1.5, -4) \)[/tex].
Therefore, the midpoint of the line segment with endpoints [tex]\((-4, -3)\)[/tex] and [tex]\((7, -5)\)[/tex] is [tex]\( \boxed{(1.5, -4)} \)[/tex]. Hence, the correct answer is:
C. [tex]\((1.5, -4)\)[/tex]
