Equation X=0: Identifying the Plane

In a three-dimensional coordinate system, points are represented by three coordinates: $(\text{x}, \text{y}, \text{z})$. Each coordinate describes the position of a point along a specific axis:

• The x-coordinate describes the position along the X-axis.
• The y-coordinate describes the position along the Y-axis.
• The z-coordinate describes the position along the Z-axis.

Understanding X=0 in 3D Space

When we are given an equation like $\text{X} = 0$, it means that we are looking for all points $(\text{x}, \text{y}, \text{z})$ where the value of the x-coordinate is always zero. This condition restricts the position of the point. If $\text{x} = 0$, the point cannot move along the X-axis away from the origin (0,0,0) in the x-direction. The point will always be located on a surface where its distance from the YZ-plane along the X-axis is zero.

YZ-Plane Representation

Consider a point in 3D space where the x-coordinate is fixed at zero. The y-coordinate and the z-coordinate, however, can take any real value. This defines a flat surface that extends infinitely in the Y and Z directions while always passing through the origin along the X-axis (since X is 0).

This specific flat surface is known as the YZ-plane. All points on the YZ-plane have an x-coordinate of 0. For example, points like $(\text{0}, \text{5}, \text{2})$, $(\text{0}, \text{-1}, \text{10})$, and $(\text{0}, \text{0}, \text{0})$ all lie on the YZ-plane because their x-coordinate is 0. The YZ-plane contains both the Y-axis and the Z-axis, as for any point on either of these axes, the x-coordinate is 0.

Why Other Options Are Incorrect

• XY — Plane: The XY-plane is defined by the equation $\text{Z} = 0$. On this plane, points have coordinates $(\text{x}, \text{y}, \text{0})$, meaning their z-coordinate is zero.
• XYZ — Space: XYZ-space refers to the entire three-dimensional coordinate system itself. It is not defined by a single equation like $\text{X} = 0$, but encompasses all possible values of x, y, and z.
• XZ — Plane: The XZ-plane is defined by the equation $\text{Y} = 0$. On this plane, points have coordinates $(\text{x}, \text{0}, \text{z})$, meaning their y-coordinate is zero.

Therefore, the equation $\text{X} = 0$ uniquely represents the YZ-plane, where the x-coordinate of every point on the plane is zero.