Easily find the coordinates of a point dividing a line segment using our Internal and External Division of Line Segment Calculator. Whether it's internal division or external division, simply input the coordinates of the two endpoints and the division ratio (m:n) to instantly get the result. This tool simplifies complex section formula calculations for geometry students and professionals.
Formula:
Let the line segment be formed by points A(x1, y1) and B(x2, y2), and let point P(X, Y) divide AB in the ratio m:n.
- Internal Division Formula:
X = (n·x1 + m·x2) / (m + n)
Y = (n·y1 + m·y2) / (m + n) - External Division Formula:
X = (n·x1 - m·x2) / (n - m)
Y = (n·y1 - m·y2) / (n - m)
(Note: For external division, m ≠ n)
Where:
- x1, y1: Coordinates of the first endpoint (A)
- x2, y2: Coordinates of the second endpoint (B)
- m, n: The ratio in which the segment is divided