For a better understanding of the solution provided here please find the diagram attached.
Please note that in coordinate geometry, the coordinates of the midpoint of a line segment is always the average of the coordinates of the endpoints of that line segment.
Thus, if, for example, the end coordinates of a line segment are [tex] (x_{1}, y_1) [/tex] and [tex] (x_2, y_2) [/tex] then the coordinates of the midpoint of this line segment will be the average of the coordinates of the two endpoints and thus, it will be:
[tex] (\frac{(x_1+x_2)}{2}, \frac{(y_1+y_2)}{2}) [/tex]
Thus for our question the endpoints are [tex] (x_E, y_E) [/tex] and [tex] (x_F, y_F) [/tex] and hence the midpoint will be:
[tex] (x_M, y_M)= [/tex][tex] (\frac{(x_E+x_F)}{2}, \frac{(y_E+y_F)}{2}) [/tex]
Thus, Option C is the correct option.
