Question

The sides of a 2 × 3 × 4 rectangular solid are parallel to the coordinate planes. The coordinates of four of its vertices are (1, −2, 3), (−1, −2, −1), (−1, 1, 3), and (1, −2, 3). What are the coordinates of the other four vertices?

Short answer

The remaining coordinates of the cuboid are ( -1, -2, 3 ); ( 1, 1, 3 ); ( 1, 1, -1 ); ( 1, -2, -1 ) and ( -1, 1, -1 ).

Step-by-step solution

Step 1. Analyzing the problem

According to the coordinates given we can assume that the given vertices should be at the below mentioned locations.

From the figure, the line along x - axis will have a length of 2 units.

The line along the y - axis will have a length of 3 units.

The line along the z - axis will have a length of 4 units.

Step 2. Finding coordinates.

Coordinates of D: ( -1, -2, 3 )

Coordinates of E: ( 1, 1, 3 )

Coordinates of F: ( 1, 1, -1 )

Coordinates of G: ( 1, -2, -1 )

Coordinates of H: ( -1, 1, -1 )