If a point P lies in yz-plane, then the coordinates of a point on yz-plane is of the form ____.

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Concept understanding — Coordinate Axes Equations

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

\text{x-axis: } y = 0

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.

Watch out

A common mistake is to think $y=0$ means "the point $(0,0)$ ". No — it means every point with $y=0$ , like $(5,0)$ , $(-3,0)$ , $(100,0)$ , etc. It's a whole line, not a single point.

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." …

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A point on the $yz$ -plane has zero distance from that plane, meaning its $x$ -coordinate must be zero; the form is $(0, y, z)$ .

Understanding the Coordinate Planes

In three-dimensional space, the coordinate axes divide space into regions, and the coordinate planes are special surfaces where one coordinate is always zero.

The $yz$ -plane is the vertical plane that contains both the $y$ -axis and the $z$ -axis. Think of it as a wall standing perpendicular to the $x$ -axis. Every point on this plane shares one crucial property: it has no displacement along the $x$ -direction.

When we say a point lies "in" or "on" the $yz$ -plane, we mean it sits exactly on this surface. The $x$ -coordinate measures how far a point is from the $yz$ -plane—positive values mean the point is on one side, negative values mean it's on the other side, and zero means the point is right on the plane itself.

Finding the Form

Identify the defining condition: For a point $P(x, y, z)$ to lie on the $yz$ -plane, its perpendicular distance from this plane must be zero. This distance is measured along the $x$ -axis.
Apply the condition: The perpendicular distance from the $yz$ -plane is simply $|x|$ . For the point to be on the plane, we need $|x| = 0$ , which gives us $x = 0$ . …

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←Previous questionQ38 — The three coordinate planes divide the space into ____ parts.→Next questionQ40 — The equation of yz-plane is ____.

Q.If a point P lies in yzyzyz-plane, then the coordinates of a point on yzyzyz-plane is of the form ________.

Understanding the Coordinate Planes

Finding the Form

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Q.If a point P lies in $yz$ -plane, then the coordinates of a point on $yz$ -plane is of the form ________.

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