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. units your answer: √13 units change my answer

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 $(x_1,y_1)=(8,1)$ and $(x_2,y_2)=(5,4)$. Then $x_2 - x_1=5 - 8=- 3$ and $y_2 - y_1=4 - 1 = 3$.

Step3: Calculate the squares and sum

$(x_2 - x_1)^2=(-3)^2 = 9$ and $(y_2 - y_1)^2=3^2 = 9$. The sum is $9 + 9=18$.

Step4: Simplify the radical

$d=\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}$

Answer:

$3\sqrt{2}$