Question

Draw a rectangular box with the origin and (2, 4, 5) as opposite vertices and with its faces parallel to the coordinate planes. Label all vertices of the box.

Answer 1

(0,0,0), (2, 0, 0), (0, 4, 0), (0, 0, 5), (2, 4, 0), (0, 4, 5), (2, 0, 5), (2, 4, 5)

Explanation:

This rectangular box would have 8 vertices where:

- The 1st point is at origin (0,0,0)

- The 8th point is at (2,4,5)

Because these points are opposites and the faces are all parallel to the coordinates planes:

- 3 of the points are in the axes (2, 0, 0), (0, 4, 0) and (0, 0, 5)

- 3 of the points are in the planes (2, 4, 0), (0, 4, 5) and (2, 0 , 5)