To find the midpoint of a line segment in a coordinate plane, you use the midpoint formula. The midpoint formula for a line segment with endpoints [tex]\( M(x_1, y_1) \)[/tex] and [tex]\( N(x_2, y_2) \)[/tex] is:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Given the endpoints [tex]\( M(9, -2) \)[/tex] and [tex]\( N(-2, -6) \)[/tex], we can denote their coordinates as:
- [tex]\( x_1 = 9 \)[/tex]
- [tex]\( y_1 = -2 \)[/tex]
- [tex]\( x_2 = -2 \)[/tex]
- [tex]\( y_2 = -6 \)[/tex]
Now, let's calculate the midpoint coordinates step-by-step.
### Calculating the x-coordinate of the midpoint:
[tex]\[
\text{midpoint}_x = \frac{x_1 + x_2}{2} = \frac{9 + (-2)}{2} = \frac{9 - 2}{2} = \frac{7}{2} = 3.5
\][/tex]
### Calculating the y-coordinate of the midpoint:
[tex]\[
\text{midpoint}_y = \frac{y_1 + y_2}{2} = \frac{-2 + (-6)}{2} = \frac{-2 - 6}{2} = \frac{-8}{2} = -4
\][/tex]
Putting these values together, the coordinates of the midpoint are:
[tex]\[
(3.5, -4)
\][/tex]
So, the correct answer is:
[tex]\[
\left( 3 \frac{1}{2}, -4 \right)
\][/tex]
