Mid-point formula
- CBSE · NCERT Class 10, Ch 7 Coordinate Geometry
The mid-point formula gives the middle point of the line joining (x₁, y₁) and (x₂, y₂) as ((x₁ + x₂)/2, (y₁ + y₂)/2).
It is the section formula with the ratio 1 : 1. In words: average the x-coordinates, then average the y-coordinates.
Two facts from geometry make it a tool. The diagonals of a parallelogram bisect each other, so they share a mid-point. And the mid-point of a segment lies on its perpendicular bisector.
A small example
The mid-point of (-3, -4) and (3, 4) is ((-3 + 3)/2, (-4 + 4)/2) = (0, 0). So (0, 0) lies on the perpendicular bisector of this segment. Question 7 of CBSE's 2026-27 Maths Standard sample paper tests exactly this, for 1 mark.
Where marks go
Question 25(A) of CBSE's 2026-27 Maths Basic sample paper gives A(3, 1), B(5, 1), C(a, b) and D(4, 3) as the corners of parallelogram ABCD. It asks for a and b, for 2 marks.
The board's Maths Basic marking scheme for 2026-27 first writes that the mid-point of AC equals the mid-point of BD. That gives (3 + a)/2 = 9/2 and (1 + b)/2 = 4/2. So a = 6 and b = 3. The scheme splits the 2 marks into half, 1 and half across these steps, in the way step marking works. The reason, that the diagonals bisect each other, is written into its first line. The corner order matters too: in ABCD, the diagonals are AC and BD.
Sources
Facts last checked against these sources on 30 September 2026.
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