Question

Which of the following ordered triples represent other vertices of the right prism with a rhombus base, where one vertex is located at (4, 0, 2)? Select three options from the following:

A) (−4, 0, −2).
B) (0, −3, 2).
C) (0, −3, 0).
D) (−4, 0, 2).
E) (0, 3, −2).

Answer 1

The other vertices of the right prism with a rhombus base can be found by changing the sign or magnitude of the coordinates.

Step-by-step explanation:

The right prism with a rhombus base has three pairs of opposite vertices that have equal coordinates except for a change in sign or magnitude. Since one vertex is located at (4, 0, 2), the other vertices must have coordinates that are either signed or equal in magnitude but opposite in sign.

Therefore, the options that represent other vertices are:

1. (−4, 0, −2) - the coordinates are opposite in sign to the given vertex
2. (0, −3, 0) - the x-coordinate is equal in magnitude but opposite in sign to the given vertex
3. (0, 3, −2) - the x-coordinate is equal in magnitude but opposite in sign to the given vertex