Distance formula
- CBSE · NCERT Class 10, Ch 7 Coordinate Geometry
The distance formula gives the length between the points (x₁, y₁) and (x₂, y₂) as √[(x₂ - x₁)² + (y₂ - y₁)²].
It is Pythagoras' theorem on a graph. The difference in x is one side of a right triangle. The difference in y is the other. The distance is the longest side. The distance of a point (x, y) from the origin is √(x² + y²).
It does not matter which point you call the first. The differences are squared, so their signs drop out.
A small example
Find the distance between (1, 2) and (4, 6). The differences are 4 - 1 = 3 and 6 - 2 = 4. So the distance is √(9 + 16) = √25 = 5 units.
Where marks go
Question 25(B) of CBSE's 2026-27 Maths Basic sample paper asks for a relation between x and y. The point P(x, y) must be the same distance from A(1, 4) and B(-1, 2). The board's Maths Basic marking scheme for 2026-27 gives half a mark for writing PA = PB with the distance formula. It gives 1 mark for squaring and expanding, and half a mark for x + y = 3.
Squaring both sides removes the roots, and the x² and y² terms cancel. With a negative point, take care with signs: x - (-1) is x + 1. The first half mark rests on setting up PA = PB at all. Each step after it is marked on its own under step marking.
Sources
Facts last checked against these sources on 30 September 2026.
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