Ratios Of Directed Line Segments Calculator

Section Formula for Directed Line Segments:

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

Point A X-coordinate (x₁):

Point A Y-coordinate (y₁):

Point B X-coordinate (x₂):

Point B Y-coordinate (y₂):

Ratio m (AP:PB):

Ratio n (AP:PB):

Result:

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1. What is the Ratio of Directed Line Segments?

The ratio of directed line segments describes how a point divides a line segment into two parts. Given points A and B, a point P divides AB in the ratio m:n, meaning AP:PB = m:n.

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:

\( A(x_1, y_1) \) — First point coordinates
\( B(x_2, y_2) \) — Second point coordinates
\( m:n \) — Ratio in which point P divides AB

Explanation: The formula calculates the coordinates of point P that divides the line segment AB internally in the given ratio.

3. Importance of Section Formula

Details: The section formula is fundamental in coordinate geometry for finding points that divide line segments in specific ratios, used in physics, engineering, and computer graphics.

4. Using the Calculator

Tips: Enter coordinates of points A and B, and the ratio m:n. The calculator will find point P that divides AB in the given ratio.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between internal and external division?
A: Internal division means P is between A and B. For external division (negative ratios), P lies outside AB.

Q2: What if m:n is 1:1?
A: When m:n = 1:1, P is the midpoint of AB.

Q3: Can the ratio be negative?
A: Yes, negative ratios indicate external division, but this calculator handles only positive ratios (internal division).

Q4: How is this different from finding a point along a line?
A: The section formula gives exact position based on ratio, while parametric equations use distance or percentage.

Q5: What are practical applications?
A: Used in computer graphics, game development, physics simulations, and any application requiring precise positioning.