Question

find the distance between the points (6, -1) and (-2, -7). write your answer as a whole number or a fully simplified radical expression. do not round.

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, $x_1 = 6,y_1=-1,x_2=-2,y_2 = - 7$.

Step2: Substitute values

$d=\sqrt{(-2 - 6)^2+(-7+1)^2}=\sqrt{(-8)^2+(-6)^2}$.

Step3: Calculate squares

$d=\sqrt{64 + 36}=\sqrt{100}$.

Step4: Simplify square - root

$d = 10$.

Answer:

10