Line Segment Calculator
Line Segment Calculator 📏
Calculate all parameters of a line segment between two points on the coordinate plane. Find length, midpoint, division point in given ratio, and slope angle.
📐 Essential Formulas
- Length: d = √[(x₂-x₁)² + (y₂-y₁)²]
- Midpoint: M((x₁+x₂)/2, (y₁+y₂)/2)
- Division in ratio m:n: P((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))
- Slope angle: α = arctan((y₂-y₁)/(x₂-x₁))
🎯 What you can calculate:
- ✅ Segment length from endpoint coordinates
- ✅ Midpoint coordinates of the segment
- ✅ Division point in a given ratio
- ✅ Slope angle with respect to x-axis
- ✅ Line equation passing through the points
- ✅ Distance from point to the line
📚 Applications:
Used in coordinate geometry, computer graphics, GPS navigation, architectural design, and physics for motion analysis.
Frequently Asked Questions
How to find the length of a line segment?
Use the distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²]. This comes from the Pythagorean theorem applied to the right triangle formed by the coordinates.
What is the midpoint of a segment?
The midpoint is the point that divides the segment into two equal parts. Its coordinates are: M((x₁+x₂)/2, (y₁+y₂)/2).
How to divide a segment in a given ratio?
To divide segment AB in ratio m:n, the division point P has coordinates: P((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)).
What does the slope angle mean?
The slope angle is the angle between the line segment and the positive direction of the x-axis, measured from 0° to 180°.
How to find the equation of a line through two points?
Use the point-slope form: y - y₁ = m(x - x₁), where m = (y₂-y₁)/(x₂-x₁) is the slope.