Understand and calculate the point that divides a line segment in a specific ratio. This tool applies the section formula for both internal and external divisions, simplifying complex geometry problems instantly. Perfect for students and professionals in mathematics and engineering.
Formula:
To find the coordinates of point P(x, y) that divides the line segment AB, with A(x1, y1) and B(x2, y2), in the ratio m:n:
Internal Division Formula:
x = (m · x2 + n · x1) / (m + n)
y = (m · y2 + n · y1) / (m + n)
External Division Formula:
x = (m · x2 - n · x1) / (m - n)
y = (m · y2 - n · y1) / (m - n)
Note: Division by zero (e.g., m + n = 0 or m - n = 0) indicates an invalid ratio for a finite point of division.