Section formula
- CBSE · NCERT Class 10, Ch 7 Coordinate Geometry
The section formula gives the point that divides the line joining (x₁, y₁) and (x₂, y₂) internally in the ratio m₁ : m₂.
The point is ((m₁x₂ + m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂)). Note the cross pairing: m₁ goes with the second point, and m₂ with the first. When the ratio is unknown, call it k : 1. Then the point is ((kx₂ + x₁)/(k + 1), (ky₂ + y₁)/(k + 1)).
The mid-point formula is the special case where the ratio is 1 : 1.
A small example
Find the point that divides the join of A(1, 2) and B(7, 8) in the ratio 1 : 2. Then x = (1 × 7 + 2 × 1)/3 = 3 and y = (1 × 8 + 2 × 2)/3 = 4. The point is (3, 4).
Where marks go
Question 30 of CBSE's 2026-27 Maths Standard sample paper asks in what ratio the x-axis divides the join of (-4, -6) and (-1, 7). It also asks for the point. The board's Maths Standard marking scheme for 2026-27 takes the ratio as k : 1. It gives 1 mark for the point's coordinates in terms of k.
Any point on the x-axis has y = 0. So (7k - 6)/(k + 1) = 0, which gives k = 6/7 for half a mark. Half a mark is for the ratio 6 : 7, and 1 mark for the point (-34/13, 0). So the fact that y = 0 on the x-axis is the key step after the first mark. See how step marking splits a 3-mark answer.
Sources
Facts last checked against these sources on 30 September 2026.
About the author
Chief Architect
An engineer (B.Tech, Computer Science) with over 20 years of preparing students for entrance exams, including as Dean at FIITJEE and Vice-President at Aakash. He is the chief architect of the TRUpreBoards evaluation engine.
Mohit Sardana on LinkedIn
