find the coordinates of the midpoint of the segment.

Answer

First, assume the endpoints of the line - segment:
- Let the endpoints of the line - segment be ((x_1,y_1)) and ((x_2,y_2)). From the graph, if we assume the left - hand endpoint is ((x_1,y_1)=(- 10,4)) and the right - hand endpoint is ((x_2,y_2)=(-8,2)).
Then, use the mid - point formula:
- The mid - point formula for two points ((x_1,y_1)) and ((x_2,y_2)) in a coordinate plane is (M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})).
- Calculate the x - coordinate of the mid - point:
  - Substitute (x_1=-10) and (x_2 = - 8) into the x - coordinate part of the formula (\frac{x_1 + x_2}{2}). We have (\frac{-10+( - 8)}{2}=\frac{-10 - 8}{2}=\frac{-18}{2}=-9).
- Calculate the y - coordinate of the mid - point:
  - Substitute (y_1 = 4) and (y_2=2) into the y - coordinate part of the formula (\frac{y_1 + y_2}{2}). We get (\frac{4 + 2}{2}=\frac{6}{2}=3).

((-9,3))