Directed Line Segment Calculation

Directed Segment Partition Formula:

\[ P = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \]

Point A (x₁):

Point A (y₁):

Point B (x₂):

Point B (y₂):

Ratio (m):

Ratio (n):

Partition Point:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Directed Segment Partition?

Directed segment partition calculates a point that divides a line segment between two points (A and B) in a given ratio m:n. The ratio is measured from point A to point B.

2. How Does the Calculator Work?

The calculator uses the section formula:

\[ P = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) \]

Where:

\( (x_1,y_1) \) — Coordinates of point A
\( (x_2,y_2) \) — Coordinates of point B
\( m:n \) — Partition ratio
\( P \) — The calculated partition point

Explanation: The formula finds a point that divides the segment AB in the ratio m:n, where m is the weight for point B and n is the weight for point A.

3. Applications of Segment Partition

Details: This calculation is fundamental in geometry, computer graphics, physics (center of mass), and engineering applications where proportional division is needed.

4. Using the Calculator

Tips: Enter coordinates for both points and the desired ratio. The ratio values must be positive numbers (they can be decimals).

5. Frequently Asked Questions (FAQ)

Q1: What does the ratio m:n represent?
A: The ratio represents how the segment is divided. For example, 1:1 gives the midpoint, 2:1 divides the segment into two parts where one is twice as long as the other.

Q2: Can I use negative ratios?
A: No, this calculator uses positive ratios only. Negative ratios would represent external division of the segment.

Q3: How is this different from simple interpolation?
A: This is a weighted interpolation where the ratio determines how much influence each endpoint has on the result.

Q4: What if m + n equals zero?
A: The calculator prevents this as it would be mathematically undefined (division by zero).

Q5: Can I use this for 3D coordinates?
A: This calculator is for 2D only, but the formula extends to 3D by adding a z-coordinate component.