Question

find the distance between the points (1, -6) and (-8, 1). 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, $x_1 = 1,y_1=-6,x_2=-8,y_2 = 1$.

Step2: Substitute values

$d=\sqrt{(-8 - 1)^2+(1-(-6))^2}=\sqrt{(-9)^2+(1 + 6)^2}=\sqrt{81+49}$.

Step3: Simplify

$d=\sqrt{130}$.

Answer:

$\sqrt{130}$