Question

The octant in which the point (2,-4,-7) lies is

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

Answer 1

The Correct Option is A

To determine the octant in which the point (2, -4, -7) lies, we need to consider the signs of its coordinates.
In an octant, the x, y, and z coordinates can have either positive (+) or negative (-) values.

Given the point (2, -4, -7), we can determine the octant as follows:
First, consider the x-coordinate, which is 2. Since it is positive, we eliminate the octants with negative x-values (4^th, 5^th, 6^th, and 7^th).
Next, consider the y-coordinate, which is -4. Since it is negative, we eliminate the octants with positive y-values (1^st, 2^nd, 5^th, and 6^th).
Lastly, consider the z-coordinate, which is -7. Since it is negative, we eliminate the octants with positive z-values (1^st, 2^nd, 3^rd, and 4^th).

Based on the elimination process, we find that the point (2, -4, -7) lies in the Eighth octant.
Therefore, the octant in which the point (2, -4, -7) lies is the Eighth octant (option A).

Answer 2

The point is (2, -4, -7) 
→ x > 0, y < 0, z < 0

In 3D geometry, space is divided into **8 octants** based on the signs of x, y, and z:

• First octant: x > 0, y > 0, z > 0
• Second octant: x < 0, y > 0, z > 0
• Third octant: x < 0, y < 0, z > 0
• Fourth octant: x > 0, y < 0, z > 0
• Fifth octant: x > 0, y > 0, z < 0
• Sixth octant: x < 0, y > 0, z < 0
• Seventh octant: x < 0, y < 0, z < 0
• Eighth octant: x > 0, y < 0, z < 0

So, the point (2, -4, -7) lies in the Eighth octant.

Correct answer: Eighth

Answer 3

The octants in 3D space are defined by the signs of the x, y, and z coordinates.

The signs for each octant are as follows:

• Octant I: (+, +, +)
• Octant II: (-, +, +)
• Octant III: (-, -, +)
• Octant IV: (+, -, +)
• Octant V: (+, +, -)
• Octant VI: (-, +, -)
• Octant VII: (-, -, -)
• Octant VIII: (+, -, -)

The point (2, -4, -7) has signs (+, -, -). Comparing this to the table, we see that it corresponds to Octant VIII (Eighth Octant).

Therefore, the octant in which the point (2, -4, -7) lies is the Eighth octant.

Answer: Eighth