📏 Ratios of Directed Line Segments Calculator
Calculate the ratio in which a point divides a line segment
Point P₁ (x₁, y₁)
Point P₂ (x₂, y₂)
Dividing Point P (x, y)
How to Use This Calculator
Enter Endpoints
Input coordinates (x₁, y₁) and (x₂, y₂) of the line segment endpoints.
Enter Dividing Point
Input coordinates (x, y) of the point that divides the line segment.
Calculate
Press "Calculate Ratio" to find the ratio m:n in which the point divides the segment.
Formula
Section Formula: x = (mx₂ + nx₁)/(m + n), y = (my₂ + ny₁)/(m + n)
where m:n is the ratio in which point P divides segment P₁P₂
About Ratios of Directed Line Segments Calculator
The Ratios of Directed Line Segments Calculator finds the ratio m:n in which a point divides a line segment using the section formula.
When to Use This Calculator
- Geometry: Calculate section ratios in coordinate geometry
- Mathematics: Solve problems involving line segment division
- Engineering: Analyze ratios in designs
Frequently Asked Questions
What is the section formula?
The section formula finds coordinates of a point dividing a line segment in ratio m:n: x = (mx₂ + nx₁)/(m + n), y = (my₂ + ny₁)/(m + n). For midpoint, m = n = 1 gives x = (x₁ + x₂)/2, y = (y₁ + y₂)/2.
What does ratio m:n mean?
Ratio m:n means the point divides the segment such that distance from P₁ to P is m parts, and distance from P to P₂ is n parts. The ratio describes how the point divides the line segment.