# 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

Clarisse and Lorraine, two chickens, 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 smallest distance between them?