The coordinates of a point are the perpendicular distance from the ____ on the respectives axes.

NCERT Exemplar · Q37

Q. The coordinates of a point are the perpendicular distance from the ________ on the respectives axes.

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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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The coordinates of a point are its perpendicular distances from the three coordinate planes (YZ, ZX and XY), each laid off on the respective axis.

What a Coordinate Really Measures

In space the three coordinate planes are the YZ-plane ( $x=0$ ), the ZX-plane ( $y=0$ ) and the XY-plane ( $z=0$ ). For a point $P(x,y,z)$ , each coordinate records how far $P$ is from one of these planes:

The $x$ -coordinate is the perpendicular distance of $P$ from the YZ-plane, marked off along the $x$ -axis.
The $y$ -coordinate is the perpendicular distance of $P$ from the ZX-plane, marked off along the $y$ -axis.
The $z$ -coordinate is the perpendicular distance of $P$ from the XY-plane, marked off along the $z$ -axis.

That is why the sentence ends with "on the respective axes": we measure the distance from a plane but read the value on the matching axis. …

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Q.The coordinates of a point are the perpendicular distance from the ________ on the respectives axes.

What a Coordinate Really Measures

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