Section formula: P = ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n))
The section formula is P = ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)).
What each letter means
- \(A(x_1,\ y_1),\ B(x_2,\ y_2)\) the ends of the segment
- \(m:n\) the ratio AP : PB in which P divides AB internally
When to use it
To find the point that divides a line segment in a given ratio, or (with ratio k : 1) the ratio in which an axis or a line cuts a segment.
Worked example
Find the point that divides the line segment joining \(A(-1,7)\) and \(B(4,-3)\) in the ratio \(2:3\).
- \(x=\dfrac{2(4)+3(-1)}{2+3}=\dfrac55\)
- \(y=\dfrac{2(-3)+3(7)}{2+3}=\dfrac{15}{5}\)
Answer: \((1,\ 3)\)
Common mistake
Pairing m with x₁. The m (the part next to A) multiplies the coordinates of B.
On your course
| Course | In the exam |
|---|---|
| Class 10 | Learn it: CBSE gives no formula booklet |
From our own CBSE Maths formula sheets, in our words.
Practise and revise
- Practise Class 10 Coordinate Geometry MCQs
- Revise Class 10 Coordinate Geometry
- Print Class 10 one-page formula sheet
Questions
What is the section formula?
The section formula is P = ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)). A(x₁, y₁), B(x₂, y₂): the ends of the segment; m:n: the ratio AP : PB in which P divides AB internally.
Is the section formula given in the exam?
Class 10: learn it: CBSE gives no formula booklet. This comes from our own CBSE Maths formula sheets; your teacher has the official booklet.
How does the section formula give the midpoint?
Put m = n = 1. The point becomes ((x₁ + x₂)/2, (y₁ + y₂)/2), the midpoint.
Our own wording, examples and card, checked by CBSE Math Revision. Not produced or endorsed by CBSE or NCERT.