Master coordinate geometry with our Division of Line Segment Calculator. Quickly determine the coordinates of a point that divides any line segment in a given ratio, whether internally or externally. Input your endpoint coordinates and the desired ratio to get instant, accurate results for geometry problems.
Formula:
Formula for Division of a Line Segment
For a line segment with endpoints A(x1, y1) and B(x2, y2), divided by a point P(x, y) in the ratio m:n, the coordinates are:
- Internal Division:
x = (m·x2 + n·x1) / (m + n)
y = (m·y2 + n·y1) / (m + n)
- External Division:
x = (m·x2 - n·x1) / (m - n)
y = (m·y2 - n·y1) / (m - n)
Where:
- (x1, y1) = Coordinates of the first endpoint
- (x2, y2) = Coordinates of the second endpoint
- m:n = The given division ratio (e.g., 2:3)