Question

find the distance between the points (-1, -8) and (8, -9). write your answer as a whole number or a fully simplified radical expression. do not round.

Explanation:

Step1: Identify the 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: Assign the values of the points

Let $(x_1,y_1)=(-1,-8)$ and $(x_2,y_2)=(8,-9)$. Then $x_2 - x_1=8-(-1)=9$ and $y_2 - y_1=-9 - (-8)=-1$.

Step3: Substitute into the formula

$d=\sqrt{(9)^2+(-1)^2}=\sqrt{81 + 1}=\sqrt{82}$.

Answer:

$\sqrt{82}$