Question

find the distance between the points (-2, -1) and (-1, -6). 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, $x_1=-2,y_1 = - 1,x_2=-1,y_2=-6$.

Step2: Substitute values

$d=\sqrt{(-1-(-2))^2+(-6 - (-1))^2}=\sqrt{(-1 + 2)^2+(-6 + 1)^2}=\sqrt{(1)^2+(-5)^2}$.

Step3: Calculate squares and sum

$\sqrt{1 + 25}=\sqrt{26}$.

Answer:

$\sqrt{26}$