Q. 6 - Calculus

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? 

Step-by-Step Solution

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 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 )