Question

find the distance between the points (-2, -8) and (2, -7). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Identify distance formula

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

Step2: Substitute the given points

Here $x_1=-2,y_1 = - 8,x_2=2,y_2=-7$. So $d=\sqrt{(2-(-2))^2+((-7)-(-8))^2}$.

Step3: Simplify the expressions inside the square - root

First, $2-(-2)=2 + 2=4$ and $(-7)-(-8)=-7 + 8 = 1$. Then $d=\sqrt{4^2+1^2}=\sqrt{16 + 1}$.

Step4: Calculate the final result

$d=\sqrt{17}$.

Answer:

$\sqrt{17}$