What it does
In space a point needs three numbers: how far along x, along y and up z. Drawings of 3D axes on flat paper are hard to read, so this page lets you turn the axes round with your finger and watch where a point really is.
- Place two points P and Q with the x, y and z sliders. The dashed coordinate box behind each point shows its three coordinates as edges: walk x along the x axis, y across, then z up.
- The page names the octant of each point from the signs of its coordinates. The three coordinate planes cut space into eight octants, numbered I to VIII: I is (+, +, +), II (−, +, +), III (−, −, +), IV (+, −, +), and V to VIII are the same four below the xy plane. A point with a zero coordinate lies on a plane or an axis and is in no octant.
- The distance formula in 3D is worked with your numbers: PQ = √[(x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²], and so is the distance from the origin.
- Tick the box for the section formula: R divides PQ in the ratio m : n, and the page checks PR : RQ for you.
It follows the Class 11 chapter introduction to three-dimensional geometry and gets you ready for Class 12 vectors and lines in space.
The flat version of all this is section formula; in Class 12 the same points become vectors in 3D vector lab, and straight lines in the plane are in line forms converter.
How to use it
- Pick P or Q under “Move”, then set x, y and z with the sliders (whole numbers from −6 to 6).
- Drag the picture to turn it, or tap Slanted, Front (yz) or Top (xy) for a standard view. In the top view you see the floor plan: x and y only.
- Untick the coordinate box if the picture gets busy.
- Tick the section formula box and set m and n to place R on PQ.
A worked example
The page starts with P(3, −2, 4) and Q(−1, 2, 2).
- P has signs (+, −, +), so it is in octant IV. Q has signs (−, +, +): octant II.
- PQ = √[(−4)² + 4² + (−2)²] = √(16 + 16 + 4) = √36 = 6.
- P is √(9 + 4 + 16) = √29 ≈ 5.3852 from the origin.
- With the section formula on and m : n = 1 : 1, R is the midpoint (1, 0, 3), and PR = RQ = 3.
Tips
- The 3D distance formula is Pythagoras twice: first across the floor, then up the height.
- Flipping the sign of z moves a point between octants I and V, II and VI, and so on.
- Points on the x axis look like (a, 0, 0); points in the yz plane look like (0, b, c).
Check yourself
Four fresh questions: a distance between two points (always a whole number), the octant of a point (type 1 to 8), a midpoint, and a distance from the origin. Nothing is saved.
FAQ
Why is x pointing towards me? That is the usual way 3D axes are drawn in school books: x out of the page, y to the right, z up. Turn the picture to see it any other way.
Is this from the NCERT book? It covers the same topics with fibub’s own examples. fibub is not part of NCERT.
Where the numbers come from
- Standard three-dimensional coordinate geometry: the three axes and coordinate planes, the eight octants (I to VIII in the usual school order), the distance formula √[(x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²] and the section formula. Written for fibub.
- Checked on hand-worked examples (computed again in Python) and on 300 random cases: the turning view keeps every distance, and R lies on PQ with PR : RQ = m : n.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.