Question

1. which statement correctly represents the distance between points e and f?

options:
$d = \sqrt{(0 - 6)^2 + (0 - 5)^2 + (5 - 5)^2}$
$d = \sqrt{(0 - 0)^2 + (0 - 6)^2 + (5 - 5)^2}$
$d = \sqrt{(0 - 0)^2 - (0 - 6)^2 - (5 - 5)^2}$
$d = \sqrt{(5 - 0)^2 + (0 - 6)^2 + (5 - 5)^2}$

Explanation:

Step1: Recall 3D distance formula

For points $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$, $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

Step2: Identify coordinates of E and F

Point E: $(0,0,5)$; Point F: $(0,6,5)$

Step3: Substitute into distance formula

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

Answer:

$d = \sqrt{(0 - 0)^2 + (0 - 6)^2 + (5 - 5)^2}$ (the second option)