Question

find the distance between the pair of points. if necessary, express answers in simplified radical form and then round to two decimal places.
(3,9) and (8,21)
the distance between the points is
(simplify your answer. type an exact answer, using radicals as needed.)

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, $(x_1,y_1)=(3,9)$ and $(x_2,y_2)=(8,21)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=8 - 3=5$, and $y_2 - y_1=21 - 9 = 12$.

Step3: Substitute into formula

Substitute into the distance formula: $d=\sqrt{(5)^2+(12)^2}=\sqrt{25 + 144}=\sqrt{169}$.

Step4: Simplify radical

Since $\sqrt{169}=13$.

Answer:

13