What is the perpendicular distance of the point (x, y) from x-axis ?

Options

A. x
B. y
C. |x|
D. |y|

Explanation

To find the perpendicular distance of the point (x, y) from the x-axis, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Equation of the X-axis**:
The equation of the x-axis is given by \( y = 0 \).

2. **Define the Point**:
We have a point \( (x, y) \) where \( x \) is the x-coordinate and \( y \) is the y-coordinate.

3. **Use the Distance Formula**:
The formula for the perpendicular distance \( D \) from a point \( (x_1, y_1) \) to a line given by the equation \( Ax + By + C = 0 \) is:
\[ D = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}} \]
In our case, the equation of the x-axis can be rewritten as:
\[ 0 \cdot x + 1 \cdot y + 0 = 0 \]
Here, \( A = 0 \), \( B = 1 \), and \( C = 0 \).

4. **Substitute the Values**:
Now, substituting \( (x_1, y_1) = (x, y) \) into the distance formula:
\[ D = \frac{|0 \cdot x + 1 \cdot y + 0|}{\sqrt{0^2 + 1^2}} \]
This simplifies to:
\[ D = \frac{|y|}{\sqrt{1}} = |y| \]

5. **Conclusion**:
Therefore, the perpendicular distance of the point \( (x, y) \) from the x-axis is \( |y| \).

### Final Answer:
The perpendicular distance of the point \( (x, y) \) from the x-axis is \( |y| \).

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