What it does
Coordinate geometry turns shapes into numbers. This page puts two points A and B on a grid and works out, with your own coordinates:
- the distance AB = √[(x₂ − x₁)² + (y₂ − y₁)²], which is just Pythagoras’ theorem on the grid;
- the point P that divides AB in the ratio m : n (the section formula), inside AB or, if you tick the box, outside it;
- the midpoint M, the special case m : n = 1 : 1;
- where the x axis cuts AB, as a ratio;
- with a third point C, the centroid G of triangle ABC and the triangle’s area.
It follows the Class 10 chapter coordinate geometry (distance formula and section formula). The area of a triangle and external division are useful extras for older syllabuses and Class 11.
The distance formula comes from pythagoras proof playground. Lines on the same grid are in the linear pairs, and you can build your own constructions in interactive geometry construction.
How to use it
- Drag A and B on the grid. They snap to whole-number points from −10 to 10.
- Set the ratio m : n with the sliders or boxes. The green point P moves along AB; the orange point M is the midpoint.
- Tick Divide externally to put P on the line AB beyond B (or A).
- Tick Add a third point C for the triangle, its medians (dashed), the red centroid G and the area.
- Every formula in the second card is filled in with your numbers.
A worked example
The page starts with A(−6, −4), B(6, 5) and m : n = 2 : 1.
- Distance: √[12² + 9²] = √225 = 15.
- Section point: x = (2 × 6 + 1 × (−6)) / 3 = 2 and y = (2 × 5 + 1 × (−4)) / 3 = 2, so P = (2, 2). Check: AP = 10 and PB = 5, a ratio of 2.
- Midpoint: (0/2, 1/2) = (0, 0.5).
- The x axis cuts AB in the ratio 4 : 5 from A, since A is 4 below the axis and B is 5 above it.
With C(5, −6): the centroid is (5/3, −5/3) ≈ (1.667, −1.667) and the area is ½|−6(11) + 6(−2) + 5(−9)| = 61.5.
Tips
- The section formula puts m next to B’s coordinates and n next to A’s: the point is pulled towards the end with the bigger share.
- If the area of three points is 0, they lie on one line (they are collinear).
Check yourself
Four fresh questions each time: a distance, a midpoint, a section point and a centroid. Type points as x, y (for example 2, −3), press Check, and open the worked answer if you need it. Nothing is saved.
FAQ
Can I use points beyond 10? The picture shows −10 to 10 so it stays readable on a phone; the questions use the same range.
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 coordinate geometry: the distance formula (from Pythagoras' theorem), the section formula, the midpoint and centroid formulas and the area of a triangle from its vertices. Written for fibub.
- Checked on hand-worked examples and on 300 random point sets (P lies on AB with AP : PB = m : n, the centroid is 2 : 1 along each median, the area equals the shoelace sum).
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.