Question

find the distance between the points (8, 1) and (4, 6). 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, $x_1 = 8,y_1 = 1,x_2 = 4,y_2 = 6$.

Step2: Substitute values

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

Step3: Calculate squares

$(-4)^2=16$ and $5^2 = 25$, so $d=\sqrt{16 + 25}$.

Step4: Add values inside square - root

$16+25 = 41$, so $d=\sqrt{41}$.

Answer:

$\sqrt{41}$