Question

find each of the following. (a) the distance between the two points (b) the coordinates of the midpoint of the segment having the points as endpoints (3,8) and (2,11) (a) what is the distance? (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 3,y_1 = 8,x_2=2,y_2 = 11$.

Step2: Substitute values

$d=\sqrt{(2 - 3)^2+(11 - 8)^2}=\sqrt{(-1)^2+3^2}=\sqrt{1 + 9}=\sqrt{10}$

Step3: Recall mid - point formula

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

Step4: Substitute values

$M=(\frac{3+2}{2},\frac{8 + 11}{2})=(\frac{5}{2},\frac{19}{2})$

Answer:

(a) $\sqrt{10}$
(b) $(\frac{5}{2},\frac{19}{2})$