Question

find the distance between the points (2, 8) and (6, 4). write your answer as a whole number or a fully simplified radical expression. do not round. units

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, $x_1 = 2,y_1 = 8,x_2=6,y_2 = 4$.

Step2: Substitute values

$d=\sqrt{(6 - 2)^2+(4 - 8)^2}=\sqrt{4^2+( - 4)^2}=\sqrt{16 + 16}$.

Step3: Simplify

$d=\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}$.

Answer:

$4\sqrt{2}$ units