Q.A point is in the XZ-plane. What can you say about its $y$-coordinate?

Coordinate Axes Equations

Imagine a blank sheet of paper. You want to describe exactly where a point is. The most natural way is to draw two perpendicular lines — one horizontal, one vertical — and measure distances from them. Those two lines are the coordinate axes.

The horizontal line is the x-axis. The vertical line is the y-axis. Where they cross is the origin, the point $(0,0)$.

Now, here's the key idea: every point on the x-axis has a y-coordinate of 0. Why? Because to be on that horizontal line, you haven't moved up or down at all — your vertical distance from the axis is zero. Similarly, every point on the y-axis has an x-coordinate of 0 — you haven't moved left or right from the vertical line.

That's the entire intuition. Let's make it precise.

The Equations

That's it. These are the equations of the coordinate axes.

• $y = 0$ means: "all points where the y-coordinate is zero, regardless of x." That's the entire horizontal line through the origin.
• $x = 0$ means: "all points where the x-coordinate is zero, regardless of y." That's the entire vertical line through the origin.

Why This Matters

These two equations are the foundation for everything in coordinate geometry. Every other line, curve, or shape is described relative to these axes. For example:

• The line $y = 2$ is a horizontal line parallel to the x-axis, shifted up by 2 units.
• The line $x = -3$ is a vertical line parallel to the y-axis, shifted left by 3 units.

So when you see $y = 0$ or $x = 0$, think: "the original, unshifted axes themselves."

A Quick Check

Which axis does the point $(0, 7)$ lie on?

It has $x=0$, so it's on the y-axis.

Which axis does $(-4, 0)$ lie on?

It has $y=0$, so it's on the x-axis.

That's the whole concept. Two simple equations, but they define the entire coordinate system.

The Equations of the Coordinate Axes are introduced right at the start of the NCERT Class 11 Mathematics chapter on Straight Lines, matching searches like "equation of x-axis and y-axis" or "coordinate geometry basics class 11 maths". Though simple, this idea is a common short-answer topic in CBSE boards and forms the groundwork for every later coordinate geometry and conic section problem in JEE Main.