Question

find the distance between the points (-8, -1) and (1, -5). 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, $x_1=-8,y_1 = - 1,x_2=1,y_2=-5$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=1-(-8)=9$ and $y_2 - y_1=-5 - (-1)=-4$.

Step3: Square the differences

Square the results from step 2. $(x_2 - x_1)^2=9^2 = 81$ and $(y_2 - y_1)^2=(-4)^2 = 16$.

Step4: Sum the squared - differences

Add the squared differences: $(x_2 - x_1)^2+(y_2 - y_1)^2=81 + 16=97$.

Step5: Find the distance

Take the square - root of the sum. $d=\sqrt{97}$ units.

Answer:

$\sqrt{97}$ units