Which of the following points lie on the x-axis ?
(i) A(0, 8) (ii) B(4, 0) (iii) `C(0, -3)` (iv) `D(-6, 0)`
(v) E(2, 1) (vi) `F(-2, -1)` (vii) `G(-1, 0)` (viii) `H(0, -2)`

Answer

To determine which points lie on the x-axis, we need to understand the condition for a point to be on the x-axis in the coordinate plane. A point is represented as (x, y), where 'x' is the x-coordinate and 'y' is the y-coordinate. For a point to lie on the x-axis, the y-coordinate must be 0.

Now, let's analyze each given point:

1. **Point A(0, 8)**:
- The y-coordinate is 8, which is not equal to 0.
- **Conclusion**: A does not lie on the x-axis.

2. **Point B(4, 0)**:
- The y-coordinate is 0, which satisfies the condition for lying on the x-axis.
- **Conclusion**: B lies on the x-axis.

3. **Point C(0, -3)**:
- The y-coordinate is -3, which is not equal to 0.
- **Conclusion**: C does not lie on the x-axis.

4. **Point D(-6, 0)**:
- The y-coordinate is 0, which satisfies the condition for lying on the x-axis.
- **Conclusion**: D lies on the x-axis.

5. **Point E(2, 1)**:
- The y-coordinate is 1, which is not equal to 0.
- **Conclusion**: E does not lie on the x-axis.

6. **Point F(-2, -1)**:
- The y-coordinate is -1, which is not equal to 0.
- **Conclusion**: F does not lie on the x-axis.

7. **Point G(-1, 0)**:
- The y-coordinate is 0, which satisfies the condition for lying on the x-axis.
- **Conclusion**: G lies on the x-axis.

8. **Point H(0, -2)**:
- The y-coordinate is -2, which is not equal to 0.
- **Conclusion**: H does not lie on the x-axis.

### Summary of Points on the x-axis:
- Points that lie on the x-axis: **B(4, 0)**, **D(-6, 0)**, **G(-1, 0)**.

### Final Answer:
The points that lie on the x-axis are B, D, and G.

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