Question

select the correct answer. the endpoints of $overline{ef}$ are $e(x_e,y_e)$ and $f(x_f,y_f)$. what are the coordinates of the midpoint of $overline{ef}$? a. $(\frac{x_f}{2},\frac{y_f}{2})$ b. $(\frac{x_e}{2},\frac{y_e}{2})$ c. $(\frac{x_e + x_f}{2},\frac{y_e + y_f}{2})$ d. $(\frac{x_e+(x_f)}{2},\frac{y_f}{2})$

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.
Here, $x_1=x_E,y_1 = y_E,x_2=x_F,y_2=y_F$.

Step2: Apply the formula

The mid - point of the line segment $\overline{EF}$ with endpoints $E(x_E,y_E)$ and $F(x_F,y_F)$ is $(\frac{x_E+x_F}{2},\frac{y_E + y_F}{2})$.

Answer:

C. $(\frac{x_E+x_F}{2},\frac{y_E + y_F}{2})$