Question

find the distance between the points (8, 1) and (5, 4). write your answer as a whole number or a fully - simplified radical expression. do not round.

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: Substitute the given points

Let $(x_1,y_1)=(3,1)$ and $(x_2,y_2)=(5,4)$. Then $x_2 - x_1=5 - 3 = 2$ and $y_2 - y_1=4 - 1 = 3$.

Step3: Calculate the distance

$d=\sqrt{(2)^2+(3)^2}=\sqrt{4 + 9}=\sqrt{13}$

Answer:

$\sqrt{13}$