Question

for the points (-2, 3) and (-8, 7), (a) find the exact distance between the points. (b) find the midpoint of the line segment whose endpoints are the given points. part 1 of 2 (a) the exact distance between the points is. part 2 of 2 (b) the midpoint is.

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, $x_1=-2,y_1 = 3,x_2=-8,y_2 = 7$.

Step2: Substitute values

$d=\sqrt{(-8-(-2))^2+(7 - 3)^2}=\sqrt{(-8 + 2)^2+4^2}=\sqrt{(-6)^2+4^2}=\sqrt{36 + 16}=\sqrt{52}=2\sqrt{13}$

Step3: Recall mid - point formula

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

Step4: Substitute values

$(\frac{-2+( - 8)}{2},\frac{3 + 7}{2})=(\frac{-2-8}{2},\frac{10}{2})=(-5,5)$

Answer:

(a) $2\sqrt{13}$
(b) $(-5,5)$