Distance of the point `(4, A)` from X-axis is half its distance from Y-axis, then A=

Options

A. 2
B. 8
C. 4
D. 6

Answer

To solve the problem, we need to find the value of \( A \) such that the distance of the point \( (4, A) \) from the X-axis is half its distance from the Y-axis.

### Step-by-Step Solution:

1. **Understanding Distances**:
- The distance of a point \( (x, y) \) from the X-axis is given by the absolute value of its y-coordinate, which is \( |y| \).
- The distance of a point \( (x, y) \) from the Y-axis is given by the absolute value of its x-coordinate, which is \( |x| \).

2. **Applying to Our Point**:
- For the point \( (4, A) \):
- The distance from the X-axis is \( |A| \).
- The distance from the Y-axis is \( |4| = 4 \).

3. **Setting Up the Equation**:
- According to the problem, the distance from the X-axis is half the distance from the Y-axis:
\[ |A| = \frac{1}{2} \times 4 \]

4. **Calculating the Right Side**:
- Simplifying the right side:
\[ |A| = 2 \]

5. **Finding Possible Values for A**:
- The absolute value equation \( |A| = 2 \) gives us two possible solutions:
\[ A = 2 \quad \text{or} \quad A = -2 \]

6. **Conclusion**:
- Thus, the values of \( A \) that satisfy the condition are \( A = 2 \) or \( A = -2 \).

### Final Answer:
The possible values of \( A \) are \( 2 \) and \( -2 \).

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