Question

the endpoints of \\(\overline{cd}\\) are \\(c(3, -5)\\) and \\(d(7, 9)\\).

the coordinates of the midpoint \\(m\\) of \\(\overline{cd}\\) are (\\(\square\\), \\(\square\\)).

Explanation:

Step1: Recall midpoint formula

The midpoint $M(x,y)$ of a segment with endpoints $(x_1,y_1)$ and $(x_2,y_2)$ is given by:
$$x=\frac{x_1+x_2}{2}, \quad y=\frac{y_1+y_2}{2}$$

Step2: Substitute x-coordinates

Plug $x_1=3$, $x_2=7$ into x-formula:
$$x=\frac{3+7}{2}=\frac{10}{2}=5$$

Step3: Substitute y-coordinates

Plug $y_1=-5$, $y_2=9$ into y-formula:
$$y=\frac{-5+9}{2}=\frac{4}{2}=2$$

Answer:

$(5, 2)$