The angle between the lines `xy=0` is

Options

A. `45^(@)`
B. `30^(@)`
C. `90^(@)`
D. `180^(@)`

Answer

To find the angle between the lines represented by the equation \(xy = 0\), we can break down the problem step by step.

### Step-by-Step Solution:

1. **Understanding the Equation**:
The equation \(xy = 0\) can be interpreted as the product of \(x\) and \(y\) being zero. This means that either \(x = 0\) or \(y = 0\).

2. **Identifying the Lines**:
From the equation \(xy = 0\):
- The line \(x = 0\) represents the **Y-axis**.
- The line \(y = 0\) represents the **X-axis**.

3. **Visualizing the Lines**:
If we visualize the coordinate axes:
- The Y-axis is a vertical line.
- The X-axis is a horizontal line.

4. **Finding the Angle Between the Lines**:
The angle between the X-axis and the Y-axis can be determined by observing their orientation:
- The X-axis and Y-axis intersect at the origin (0,0).
- The angle formed between these two axes is a right angle.

5. **Conclusion**:
Therefore, the angle between the lines represented by \(xy = 0\) is \(90^\circ\).

### Final Answer:
The angle between the lines \(xy = 0\) is \(90^\circ\).

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