The set of points (x,y,z) such that x=5 is

Options

A. a point
B. a line
C. a plane
D. a circle

Explanation

To solve the question, we need to determine the geometric representation of the set of points \((x, y, z)\) such that \(x = 5\).

### Step-by-step Solution:

1. **Understanding the Equation**:
The equation \(x = 5\) specifies that the x-coordinate of every point in the set is fixed at 5. This means that no matter what values \(y\) and \(z\) take, the x-coordinate will always be 5.

**Hint**: Think of what happens when you fix one coordinate in a three-dimensional space.

2. **Visualizing the Points**:
In a three-dimensional coordinate system (x, y, z), if we fix \(x = 5\), we can visualize this as a vertical plane that extends infinitely in the y and z directions. This plane is parallel to the yz-plane and is located 5 units away from the origin along the x-axis.

**Hint**: Consider how planes are defined in three-dimensional space and how fixing one coordinate affects the other two.

3. **Identifying the Plane**:
The set of points \((5, y, z)\) where \(y\) and \(z\) can take any real number values describes a plane. This plane can be described as all points where the x-coordinate is 5, while the y and z coordinates can vary freely.

**Hint**: Remember that a plane in three-dimensional space can be defined by a linear equation involving two variables.

4. **Conclusion**:
Therefore, the set of points \((x, y, z)\) such that \(x = 5\) is a plane in three-dimensional space.

**Final Answer**: The set of points \((x, y, z)\) such that \(x = 5\) is a **plane**.