Question

using the midpoint and distance formulas, calculate the coordinate of the midpoint and the length of the segment. length of segment $overline{ab}$ coordinates of midpoint a. 8 b. 5 c. (2.5,3) d. (2,2)

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here, $x_1 = 1,y_1 = 1,x_2=4,y_2 = 5$.
$M=(\frac{1 + 4}{2},\frac{1+5}{2})=(\frac{5}{2},3)=(2.5,3)$

Step2: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
$d=\sqrt{(4 - 1)^2+(5 - 1)^2}=\sqrt{3^2+4^2}=\sqrt{9 + 16}=\sqrt{25}=5$

Answer:

Length of Segment $\overline{AB}$: b. 5
Coordinates of Midpoint: c. $(2.5,3)$