Question

find the distance between the two points in simplest radical form. (-9,9) and (0,-3)

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, $x_1=-9,y_1 = 9,x_2 = 0,y_2=-3$.

Step2: Substitute values

$d=\sqrt{(0-(-9))^2+((-3)-9)^2}=\sqrt{(0 + 9)^2+(-12)^2}=\sqrt{9^2+(-12)^2}$.

Step3: Calculate squares

$\sqrt{81 + 144}=\sqrt{225}$.

Step4: Simplify square - root

$\sqrt{225}=15$.

Answer:

$15$