The point `(-4,0,7) lies on the

Options

A. y- axis
B. xy plane
C. yz plane
D. xz plane

Explanation

To determine the plane in which the point \((-4, 0, 7)\) lies, we need to analyze its coordinates:

1. **Identify the coordinates**: The point is given as \((-4, 0, 7)\). Here, the coordinates are:
- \(x = -4\)
- \(y = 0\)
- \(z = 7\)

2. **Understanding the planes**:
- **XY-plane**: This plane consists of all points where \(z = 0\). Since our point has \(z = 7\), it does not lie on the XY-plane.
- **YZ-plane**: This plane consists of all points where \(x = 0\). Our point has \(x = -4\), so it does not lie on the YZ-plane.
- **XZ-plane**: This plane consists of all points where \(y = 0\). Our point has \(y = 0\), which means it lies on the XZ-plane.
- **X-axis**: This consists of all points where \(y = 0\) and \(z = 0\). Since our point has \(z = 7\), it does not lie on the X-axis.

3. **Conclusion**: Since the point has a specific value for \(x\) and \(z\) but \(y = 0\), we conclude that the point \((-4, 0, 7)\) lies in the XZ-plane.

**Final Answer**: The point \((-4, 0, 7)\) lies on the XZ-plane.

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