Question

find the midpoint of the line segment joining the points ( p_1 ) and ( p_2 ).( p_1 = (5, -4); p_2 = (7, 6) ) the midpoint of the line segment joining the points ( p_1 ) and ( p_2 ) is \\(\square\\). (simplify your answer. type an ordered pair.)

Explanation:

Step1: Recall midpoint formula

The midpoint $M=(x_m,y_m)$ of two points $P_1=(x_1,y_1)$ and $P_2=(x_2,y_2)$ is given by:
$$x_m=\frac{x_1+x_2}{2}, \quad y_m=\frac{y_1+y_2}{2}$$

Step2: Calculate x-coordinate of midpoint

Substitute $x_1=5$, $x_2=7$:
$$x_m=\frac{5+7}{2}=\frac{12}{2}=6$$

Step3: Calculate y-coordinate of midpoint

Substitute $y_1=-4$, $y_2=6$:
$$y_m=\frac{-4+6}{2}=\frac{2}{2}=1$$

Answer:

$(6, 1)$