Question

The endpoints of `bar(EF)` are E(xE , yE) and F(xF , yF). What are the coordinates of the midpoint of `bar(EF)`?

Answer 1

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 $(x_{1}, y_1)$ and $(x_2, y_2)$ 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:

$(\frac{(x_1+x_2)}{2}, \frac{(y_1+y_2)}{2})$

Thus for our question the endpoints are $(x_E, y_E)$ and $(x_F, y_F)$ and hence the midpoint will be:

$(x_M, y_M)=$$(\frac{(x_E+x_F)}{2}, \frac{(y_E+y_F)}{2})$

Thus, Option C is the correct option.