Section Formula
Point dividing a segment in ratio m:n.
Key idea
Point dividing a segment in ratio m:n.
In depth
The point dividing a segment from A to B in ratio m : n is ((nx₁ + mx₂)/(m + n), (ny₁ + my₂)/(m + n)). The weights are swapped: the nearer endpoint gets the larger weight.
Worked example
The point dividing (0, 0) to (9, 6) in ratio 1 : 2 is ((2·0 + 1·9)/3, (2·0 + 1·6)/3) = (3, 2).
Formula
Real-world uses
- Locating a point that divides a route in a fixed ratio, such as a checkpoint in a race
Common mistake
Swapping m and n.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Section Formula?
Point dividing a segment in ratio m:n. It is a topic at the advanced level in Geometry.
What is the formula for Section Formula?
The key formula is ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)).
Where is Section Formula used in real life?
Real-world examples: Locating a point that divides a route in a fixed ratio, such as a checkpoint in a race.
What should I learn before Section Formula?
Make sure you are comfortable with Coordinate Proofs, the previous topic in Geometry.
What is a common mistake with Section Formula?
Swapping m and n.
How can I practise Section Formula?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Section Formula?
Move on to Area by Coordinates (Shoelace) next.
Related advanced topics in Geometry
- Heron’s Formula – Triangle area from three sides.
- Regular Polygon Area – Use apothem and perimeter.
- Arc Length of a Circle – Part of the circumference.
- Sector Area – Part of the circle’s area.
- Central and Inscribed Angles – An inscribed angle is half the central angle on the same arc.
- Chord and Tangent Properties – A tangent is perpendicular to the radius at the point of contact.