# The 3D Coordinate System Exercises

### Example 1

Draw a rectangular prism with the following points as the base: L (6, 0, 0), M (6, 0, 5), N (0, 0, 5), and O (0, 0, 0). The height of the prism is 8 units. Then find its volume.

### Example 2

The coordinates of a cube are S (0, 0, 0), T (0, 0, 4), U (4, 0, 4), V (4, 0, 0), W (0, 4, 0), X (0, 4, 4), Y (4, 4, 4), and Z (4, 4, 0). If the cube was reduced by a scale factor of 4 and translated 4 units up the y-axis, what would be the coordinates of the new cube?

### Example 3

A right square pyramid has a base at points A (6, 0, 6) B (6, 0, -2), C (-2, 0, 6), and D (-2, 0, -2). If the slant height of the pyramid is 8.06 units, what are the coordinates of the vertex?

### Example 4

Graph a rectangular prism that contains the origin (0, 0, 0) and the point G (5, 7, 3) as vertices. Then, find its volume.

### Example 5

Two chickens named Clarisse and Lorraine get into a fight. They were right next to each other, but Clarisse walks 7 feet north, 3 feet east, and flutters onto a fence that's 2 feet tall. Lorraine walks 1 foot north (to try and make up with Clarisse), but then decides against it and walks 9 feet west. What's the shortest distance between them?