Question

find the distance between the points (-5, 0) and (-3, -6). write your answer as a whole number or a fully simplified radical expression. do not round.

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-5,y_1 = 0,x_2=-3,y_2=-6$.

Step2: Substitute values

$d=\sqrt{(-3-(-5))^2+(-6 - 0)^2}=\sqrt{(-3 + 5)^2+(-6)^2}=\sqrt{(2)^2+(-6)^2}$.

Step3: Calculate squares and sum

$\sqrt{4 + 36}=\sqrt{40}$.

Step4: Simplify radical

$\sqrt{40}=\sqrt{4\times10}=2\sqrt{10}$.

Answer:

$2\sqrt{10}$