📏 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

1

Enter Endpoints

Input coordinates (x₁, y₁) and (x₂, y₂) of the line segment endpoints.

2

Enter Dividing Point

Input coordinates (x, y) of the point that divides the line segment.

3

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.