Question

find the distance between the pair of points.
(0,3\sqrt{6}) and (-3\sqrt{6},0)
the distance is
(type an exact answer, using radicals as needed. simplify your answer)

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, $x_1 = 0,y_1=3\sqrt{6},x_2=- 3\sqrt{6},y_2 = 0$.

Step2: Substitute values

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

Step3: Simplify squares

$(-3\sqrt{6})^2=(-3)^2\times(\sqrt{6})^2 = 9\times6=54$. So $d=\sqrt{54 + 54}$.

Step4: Calculate sum and simplify radical

$54+54 = 108$, and $108=36\times3$. Then $d=\sqrt{36\times3}=\sqrt{36}\times\sqrt{3}=6\sqrt{3}$.

Answer:

$6\sqrt{3}$