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 \\( \square \\).

Explanation:

Step1: Recall distance formula

The distance $d$ between points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Substitute given coordinates

Let $(x_1,y_1)=(3,7)$ and $(x_2,y_2)=(6,5)$. Substitute values:
$d=\sqrt{(6-3)^2+(5-7)^2}$

Step3: Calculate differences

Compute the squared differences:
$d=\sqrt{(3)^2+(-2)^2}$

Step4: Simplify the expression

Calculate squares and sum, then simplify root:
$d=\sqrt{9+4}=\sqrt{13}$

Answer:

$\sqrt{13}$