COO006 · Coordinate geometry · Classes 10–11
Section formula
The section formula gives the point P that divides AB in the ratio m : n (AP : PB = m : n).
m : nSection formula
📐 Formula
P = ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n))
✏️ Worked example
A(−2, −1), B(4, 5), ratio 2 : 1: P = ((8 − 2)/3, (10 − 1)/3) = (2, 3).
🌍 Where it is used
Dividing a road or a plot in a given ratio; centroid formula.
❓ Quick check
Ratio 1 : 1 gives the…
🏋️ Practice
EasyDivide (0, 0)–(6, 9) in 1 : 2.
Answer: (2, 3)
MediumDivide (1, 1)–(7, 4) in 2 : 1.
Answer: (5, 3)
ChallengeWhich ratio does (3, 0) divide (0, 0)–(9, 0) in?
Answer: 1 : 2