Question

find the distance between the two points in simplest radical form.
(8,2) and (0, - 3)

Explanation:

Step1: Identify the 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, $x_1 = 8,y_1 = 2,x_2 = 0,y_2=-3$.

Step2: Substitute the values into the formula

$d=\sqrt{(0 - 8)^2+(-3 - 2)^2}=\sqrt{(-8)^2+(-5)^2}$.

Step3: Calculate the squares

$(-8)^2=64$ and $(-5)^2 = 25$, so $d=\sqrt{64 + 25}$.

Step4: Add the numbers inside the square - root

$64+25 = 89$, so $d=\sqrt{89}$.

Answer:

$\sqrt{89}$