Question

find the distance between the points (9, 3) and (3, 0). write your answer as a whole number or a fully simplified radical expression. do not round. units

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

Step2: Substitute values

$d=\sqrt{(3 - 9)^2+(0 - 3)^2}=\sqrt{(-6)^2+(-3)^2}$.

Step3: Calculate squares

$(-6)^2=36$ and $(-3)^2 = 9$, so $d=\sqrt{36 + 9}$.

Step4: Simplify

$d=\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}$.

Answer:

$3\sqrt{5}$