What Is the Y-Coordinate of Any Point on the X-Axis?
The keyword what is the y-coordinate of any point on the x-axis asks for a fundamental fact about the Cartesian coordinate plane. A point is written as an ordered pair \((x,y)\), where \(x\) measures horizontal position and \(y\) measures vertical position.
Answer: The y-coordinate of any point on the x-axis is \(0\).
Why the Y-Coordinate Must Be Zero
The x-axis is defined as the set of all points whose vertical position is zero. In coordinate notation, the x-axis is the line described by the equation \(y=0\). Therefore, every point on the x-axis has the form \((x,0)\), where \(x\) can be any real number.
Examples of Points on the X-Axis
Points such as \((-3,0)\), \((0,0)\), and \((5.7,0)\) all lie on the x-axis because their y-coordinate equals \(0\).
| Point | Y-coordinate | On the x-axis? | Reason |
|---|---|---|---|
| \((-3,0)\) | \(0\) | Yes | Matches \(y=0\) |
| \((2,0)\) | \(0\) | Yes | Matches \(y=0\) |
| \((4,1)\) | \(1\) | No | Does not satisfy \(y=0\) |
Visualization: The X-Axis as \(y=0\)
Because the x-axis is defined by the equation \(y=0\), the y-coordinate of any point on the x-axis is \(0\).