Question

find the distance between the points (-10, -9) and (2, -1). 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, $x_1=-10,y_1 = - 9,x_2=2,y_2=-1$.

Step2: Substitute values

$d=\sqrt{(2-(-10))^2+((-1)-(-9))^2}=\sqrt{(2 + 10)^2+(-1 + 9)^2}=\sqrt{12^2+8^2}$.

Step3: Calculate squares and sum

$\sqrt{144 + 64}=\sqrt{208}$.

Step4: Simplify the radical

$\sqrt{208}=\sqrt{16\times13}=4\sqrt{13}$.

Answer:

$4\sqrt{13}$ units