Question

find the distance between the points (10, 4) and (1, 6). 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Identify the points' coordinates

Here, $x_1 = 10,y_1 = 4,x_2 = 1,y_2 = 6$.

Step3: Substitute values into formula

$d=\sqrt{(1 - 10)^2+(6 - 4)^2}=\sqrt{(-9)^2+2^2}=\sqrt{81 + 4}=\sqrt{85}$.

Answer:

$\sqrt{85}$