Question

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

Explanation:

Step1: Identify the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Assign the values

Let $(x_1,y_1)=(9,3)$ and $(x_2,y_2)=(0,9)$. Then $x_2 - x_1=0 - 9=-9$ and $y_2 - y_1=9 - 3 = 6$.

Step3: Calculate the squares

$(x_2 - x_1)^2=(-9)^2 = 81$ and $(y_2 - y_1)^2=6^2=36$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=81 + 36=117$.

Step5: Find the square - root

$d=\sqrt{117}=\sqrt{9\times13}=3\sqrt{13}$.

Answer:

$3\sqrt{13}$