Question

find the distance between the points (8, 6) and (10, 1). write your answer as a whole number or a fully - simplified radical expression. do not round.

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, $x_1 = 8$, $y_1 = 6$, $x_2 = 10$, $y_2 = 1$.

Step2: Substitute values

$d=\sqrt{(10 - 8)^2+(1 - 6)^2}=\sqrt{2^2+( - 5)^2}=\sqrt{4 + 25}$.

Step3: Calculate result

$d=\sqrt{29}$

Answer:

$\sqrt{29}$