Question

1. which statement correctly represents the distance between points k and l? options: $d = \sqrt{(-5 - 0)^2 + (3 - 3)^2 + (-3 - (-3))^2}$, $d = \sqrt{(3 - 0)^2 + (-3 - 3)^2 + (5 - (-3))^2}$, $d = \sqrt{(-5 - 3)^2 + (3 - 0)^2 + (-3 - 3)^2}$, $d = \sqrt{(-5 - 3)^2 + (-3 - (-3))^2 + (-3 - 3)^2}$ (with a 3d coordinate system image showing points k, l (0,3,-3), j, m, o, p (0,0,-3), n, q (0,0,0))

Explanation:

Step1: Identify coordinates of K

From the diagram (and context, since L is (0,3,-3) and K is a vertex of the rectangular prism), we can infer K has coordinates (-5, 3, -3). L is (0, 3, -3).

Step2: Apply 3D distance formula

The 3D distance formula between two points \((x_1, y_1, z_1)\) and \((x_2, y_2, z_2)\) is \(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2}\).

Substituting \(x_1=-5, y_1 = 3, z_1=-3\) (K) and \(x_2 = 0, y_2=3, z_2=-3\) (L):

\(d=\sqrt{(-5 - 0)^2+(3 - 3)^2+(-3 - (-3))^2}\)

Step3: Match with options

The first option matches this formula.

Answer:

\(d = \sqrt{(-5 - 0)^2 + (3 - 3)^2 + (-3 - (-3))^2}\) (the first option)