To find the midpoint of the segment between the points [tex]\((8, -10)\)[/tex] and [tex]\((-10, -8)\)[/tex], we use the midpoint formula. The midpoint [tex]\((M_x, M_y)\)[/tex] of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ M_x = \frac{x_1 + x_2}{2} \][/tex]
[tex]\[ M_y = \frac{y_1 + y_2}{2} \][/tex]
Let's apply this formula step-by-step to the given points:
1. Identify the coordinates of the endpoints:
- Point 1: [tex]\( (x_1, y_1) = (8, -10) \)[/tex]
- Point 2: [tex]\( (x_2, y_2) = (-10, -8) \)[/tex]
2. Calculate the x-coordinate of the midpoint:
[tex]\[ M_x = \frac{8 + (-10)}{2} = \frac{8 - 10}{2} = \frac{-2}{2} = -1 \][/tex]
3. Calculate the y-coordinate of the midpoint:
[tex]\[ M_y = \frac{-10 + (-8)}{2} = \frac{-10 - 8}{2} = \frac{-18}{2} = -9 \][/tex]
So, the coordinates of the midpoint are [tex]\( (-1, -9) \)[/tex].
Thus, the midpoint of the line segment between the points [tex]\((8, -10)\)[/tex] and [tex]\((-10, -8)\)[/tex] is:
A. [tex]\((-1, -9)\)[/tex]
