Question

find the distance between the two points in simplest radical form. (8, -1) and (2, -9)

Explanation:

Step1: Identify 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, $(x_1,y_1)=(8,-1)$ and $(x_2,y_2)=(2,-9)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=2 - 8=-6$ and $y_2 - y_1=-9-(-1)=-9 + 1=-8$.

Step3: Square the differences

Square the results from step 2. $(-6)^2 = 36$ and $(-8)^2=64$.

Step4: Sum the squared - differences

Add the squared differences: $36 + 64 = 100$.

Step5: Calculate the square - root

$d=\sqrt{100}=10$.

Answer:

$10$