Question

find the distance between the points (3, 9) and (4, 5). 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Assign values

Let $(x_1,y_1)=(3,9)$ and $(x_2,y_2)=(4,5)$. Then $x_2 - x_1=4 - 3 = 1$ and $y_2 - y_1=5 - 9=-4$.

Step3: Substitute into formula

$d=\sqrt{(1)^2+(-4)^2}=\sqrt{1 + 16}$.

Step4: Simplify

$d=\sqrt{17}$

Answer:

$\sqrt{17}$