Question

The point (1, -3, 4) lies in the octant

• A. Second
• B. Third
• C. Fourth
• D. Eighth

Answer 1

The Correct Option is C

We need to determine which octant the point (1, -3, 4) lies in.

The signs of the coordinates in each octant are as follows:

1. (+, +, +)
2. (-, +, +)
3. (-, -, +)
4. (+, -, +)
5. (+, +, -)
6. (-, +, -)
7. (-, -, -)
8. (+, -, -)

The point (1, -3, 4) has signs (+, -, +). Comparing this to the list of octants, we see it corresponds to the 4th octant.

Therefore, the correct option is (C) Fourth.

Answer 2

The octants are determined by the signs of the coordinates $ (x, y, z) $. The signs of the given point are $ (+, -, +) $. Referring to the standard octant table:

• First octant: $ (+, +, +) $
• Second octant: $ (-, +, +) $
• Third octant: $ (-, -, +) $
• Fourth octant: $ (+, -, +) $

Thus, the point $ (1, -3, 4) $ lies in the fourth octant.

Final Answer: The final answer is $ {\text{Fourth}} $.