Q.Locate the following points:

3D Coordinate Octants

Stand at the corner of a room where two walls meet the floor. That corner is the origin $O$, and the three edges meeting there are the three coordinate axes:

• the edge where the floor meets one wall is the x-axis,
• the edge where the floor meets the other wall is the y-axis,
• the vertical edge where the two walls meet is the z-axis.

These three axes are mutually perpendicular. Taken in pairs they determine three coordinate planes — the $xy$-plane, the $yz$-plane and the $zx$-plane — and these planes slice all of space into eight regions. Each region is called an octant (from octo, meaning eight).

Why exactly eight

In a plane, the two axes make $4$ quadrants. Adding a third axis doubles this: each of the three coordinate planes splits space into two halves, so there are $2 \times 2 \times 2 = 2^3 = 8$ regions. Equivalently, an octant is fixed by choosing a sign — positive or negative — for each of $x$, $y$ and $z$, and there are $2^3 = 8$ such sign-triples $(\pm, \pm, \pm)$.

The eight octants and their signs

The standard NCERT labelling of the signs is:

Notice the pattern: octants I–IV all have $z > 0$ (above the $xy$-plane) and V–VIII all have $z < 0$ (below it).

How to read a point's octant

Just look at the signs of its coordinates. For example, $(-3, 1, 2)$ has $x < 0$, $y > 0$, $z > 0$, which is the sign pattern of octant II. The point $(-3, 1, -2)$ has $x < 0$, $y > 0$, $z < 0$, placing it in octant VI.

Why it matters

Knowing octants helps you visualise where a point sits relative to the origin, keep track of sign conventions when drawing 3D figures, and quickly sketch surfaces. It is a first step before the distance formula and later work with vectors and lines in space.

This topic sits in the NCERT Class 11 Mathematics chapter Introduction to Three Dimensional Geometry, matching searches such as "octants in 3D geometry class 11 maths" and "three dimensional geometry class 11 important questions". The same sign-based classification of space recurs in JEE Main coordinate geometry and vector algebra, where naming a point's octant at a glance saves valuable exam time.