Ratios of Directed Line Segments Calculator

Find the point dividing a segment in a given ratio (section formula).

x₁

y₁

x₂

y₂

Ratio m

Ratio n

x 4

y 2

Formula: P = ((m·x₂ + n·x₁)/(m+n), (m·y₂ + n·y₁)/(m+n))

Step-by-step with your numbers:

1. Values used:

2. x₁ = 0

3. y₁ = 0

4. x₂ = 10

5. y₂ = 5

6. Ratio m = 2

7. Ratio n = 3

9. x = 4

10. y = 2

Did we solve your problem today?

The section formula finds the point that divides a segment internally in the ratio m : n.

The math behind it

The dividing point is the weighted average of the endpoints: P = (m·B + n·A) ÷ (m + n).

From (0,0) to (10,5) in ratio 2:3 → (4, 2).

What does a 1:1 ratio give?

The midpoint of the segment.