Use this tool to easily calculate the ratios of directed line segments based on given coordinates.

## How to Use the Directed Line Segment Ratio Calculator

To use this calculator, follow these steps:

- Enter the x and y coordinates of the start point (X1, Y1).
- Enter the x and y coordinates of the end point (X2, Y2).
- Input the ratio in the form A:B as A/B. For example, for a 1:2 ratio, enter “1/2”.
- Click the “Calculate” button. The result will be displayed as a coordinate (X,Y).

## How It Works

The calculator determines the coordinates of a point dividing a directed line segment in a given ratio. The formula used is a generalization of the section formula which states:

- X = (X1 * B + X2 * A) / (A + B)
- Y = (Y1 * B + Y2 * A) / (A + B)

Where X1, Y1 are coordinates of the start point, X2, Y2 are coordinates of the end point, and A:B is the ratio.

## Limitations

This calculator has a few limitations:

- Ensure the ratio input is in the specified format (A/B).
- Ensure inputs are valid numbers to avoid unexpected results.

## Use Cases for This Calculator

### Calculate the Ratio of a Directed Line Segment

Enter the coordinates of the endpoints of the directed line segment, followed by the point dividing the segment. The calculator will determine the ratio in which the dividing point splits the line segment.

### Find the Midpoint of a Line Segment

Input the coordinates of the endpoints of the line segment. The calculator will calculate the midpoint of the line segment, providing you with the coordinates of the point that divides the segment into two equal parts.

### Determine the Length Ratio of Two Segments

Enter the coordinates of the endpoints of both line segments. The calculator will compute the ratio of the lengths of the two segments, giving you an understanding of how they compare geometrically.

### Calculate the Resultant Ratio of Two Line Segments

Input the coordinates of the endpoints of two line segments separately. The calculator will calculate the overall ratio of the combined length of these two segments, providing insight into their relationship when taken together.

### Obtain the Section Ratio Dividing Two Segments

Enter the coordinates of the endpoints of both line segments and the point that divides them individually. The calculator will determine the ratio in which the dividing point splits the combined length of the two segments.

### Calculate the Division Point of Two Segments’ Ratios

Input the ratios at which two segments are divided, along with the coordinates of the endpoints of each segment. The calculator will compute the point at which the segments intersect based on the specified ratios.

### Compare the Ratios of Multiple Line Segments

Enter the coordinates of the endpoints of multiple line segments. The calculator will compute and show you the ratios in which different segments are divided, allowing you to visually compare and analyze their proportions.

### Calculate the Ratio of Line Segments in Different Quadrants

Input the coordinates of the endpoints of line segments that lie in different quadrants. The calculator will determine the ratios of these segments accurately, taking into account the quadrant positioning to provide correct results.

### Determine the Ratio of a Segment with Negative Coordinates

Enter the coordinates of the endpoints of the line segment, including negative values if present. The calculator will handle negative coordinates correctly to calculate the ratio of the directed line segment, ensuring accuracy in the results.

### Verify Ratios of Line Segments with Decimal Coordinates

Input the coordinates of the line segments, which include decimal values. The calculator will accurately compute the ratios of the directed line segments, handling decimal points with precision to provide reliable results.