Question

1. what is the distance between points h and g? (image shows a 3d coordinate system with points: f (5,0,0), j (5,-3,0), k (5,-3,2), and a green rectangular prism. axes: x (horizontal), y (vertical), z (diagonal).)

Explanation:

Step1: Identify coordinates of H and G

First, determine the coordinates using the given points:

• Point $K$ is $(5, -3, 2)$, so point $H$ (same y,z as K, x=0) is $(0, -3, 2)$
• Point $G$ (same x as F, y,z as K) is $(5, -3, 2)$

Step2: Apply 3D distance formula

The 3D distance formula between $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ is:
$$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$$
Substitute $H(0,-3,2)$ and $G(5,-3,2)$:
$$d=\sqrt{(5-0)^2+(-3-(-3))^2+(2-2)^2}$$

Step3: Simplify the expression

Calculate each term:
$$d=\sqrt{5^2+0^2+0^2}=\sqrt{25}=5$$

Answer:

5