Which of the points A(0, 6), B(-2, 0), C(0, -5), D(3, 0) and E(1, 2) do(es) not lie on x-axis?

Options

A. A and C only
B. B and D
C. A, C and E
D. E only

Answer

To determine which points do not lie on the x-axis, we need to analyze the coordinates of each point provided:

1. **Understanding the x-axis**:
- The x-axis is defined as the line where the y-coordinate is always 0. Therefore, any point that lies on the x-axis will have coordinates in the form (x, 0).

2. **List of points**:
- A(0, 6)
- B(-2, 0)
- C(0, -5)
- D(3, 0)
- E(1, 2)

3. **Checking each point**:
- **Point A(0, 6)**: The y-coordinate is 6, which is not 0. Therefore, point A does not lie on the x-axis.
- **Point B(-2, 0)**: The y-coordinate is 0. Therefore, point B lies on the x-axis.
- **Point C(0, -5)**: The y-coordinate is -5, which is not 0. Therefore, point C does not lie on the x-axis.
- **Point D(3, 0)**: The y-coordinate is 0. Therefore, point D lies on the x-axis.
- **Point E(1, 2)**: The y-coordinate is 2, which is not 0. Therefore, point E does not lie on the x-axis.

4. **Conclusion**:
- The points that do not lie on the x-axis are A(0, 6), C(0, -5), and E(1, 2).

**Final Answer**: Points A, C, and E do not lie on the x-axis.