Question

find the distance between the points e(3, 7) and f(6, 5). answer in simplest exact form. the exact distance between the two points is

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, $x_1 = 3,y_1 = 7,x_2=6,y_2 = 5$.

Step2: Substitute values

$d=\sqrt{(6 - 3)^2+(5 - 7)^2}=\sqrt{3^2+( - 2)^2}$.

Step3: Calculate squares and sum

$d=\sqrt{9 + 4}=\sqrt{13}$.

Answer:

$\sqrt{13}$