Directed Line Segment Ratio Calculator
Find division point on directed line segment. If P divides AB in ratio m:n, then P = (n×A + m×B) / (m+n).
Formula
P = (n·A + m·B) / (m+n); divides segment AB in ratio m:n
- Section formula for internal division
- P = (n·x₁ + m·x₂)/(m+n), (n·y₁ + m·y₂)/(m+n)
- For external division: use P = (n·A - m·B) / (n-m)
- Directed segment: sign of distances shows direction
Example
Inputs
- Point A x-coordinate: 1
- Point A y-coordinate: 2
- Point B x-coordinate: 5
- Point B y-coordinate: 8
- Ratio m (part 1): 1
- Ratio n (part 2): 2
A(1,2), B(5,8), ratio 1:2: P = (2·1+1·5)/(1+2), (2·2+1·8)/(1+2) = (7/3, 4)
Frequently asked questions
What's the section formula?
Point dividing segment in ratio m:n: P = (n·A + m·B)/(m+n)
What's the difference between internal and external division?
Internal: P between A,B (ratio m:n). External: P outside (ratio -m:n or m:-n).