Question

find the distance between the points (1, 0) and (-8, -4). write your answer as a whole number or a fully simplified radical expression. do not round. units

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, $(x_1,y_1)=(1,0)$ and $(x_2,y_2)=(-8,-4)$.

Step2: Substitute values

$d=\sqrt{(-8 - 1)^2+(-4 - 0)^2}=\sqrt{(-9)^2+(-4)^2}$.

Step3: Calculate squares

$d=\sqrt{81 + 16}$.

Step4: Add inside radical

$d=\sqrt{97}$.

Answer:

$\sqrt{97}$