Question

find the distance between the points (1, -1) and (-8, -3). 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 point values

Let $(x_1,y_1)=(1,-1)$ and $(x_2,y_2)=(-8,-3)$. Then $d=\sqrt{(-8 - 1)^2+(-3+ 1)^2}$.

Step3: Simplify expressions inside square - root

First, $(-8 - 1)^2=(-9)^2 = 81$ and $(-3 + 1)^2=(-2)^2=4$. So $d=\sqrt{81 + 4}$.

Step4: Calculate final result

$d=\sqrt{85}$.

Answer:

$\sqrt{85}$