Question

find the distance between the points (5, 7) and (6, 0). 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, $x_1 = 5,y_1 = 7,x_2=6,y_2 = 0$.

Step2: Substitute values

$d=\sqrt{(6 - 5)^2+(0 - 7)^2}=\sqrt{1^2+( - 7)^2}=\sqrt{1 + 49}$.

Step3: Simplify

$d=\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$.

Answer:

$5\sqrt{2}$