Question

find the distance between the points (6, 1) and (8, 2). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Identify the 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

Here $x_1 = 6,y_1 = 1,x_2 = 8,y_2 = 2$. So $d=\sqrt{(8 - 6)^2+(2 - 1)^2}$.

Step3: Simplify the expression inside the square - root

First, $(8 - 6)^2=2^2 = 4$ and $(2 - 1)^2=1^2 = 1$. Then $d=\sqrt{4 + 1}$.

Step4: Get the final result

$d=\sqrt{5}$.

Answer:

$\sqrt{5}$