Utilize our advanced Section Formula Calculator to effortlessly determine the exact coordinates of a point dividing any given line segment. Whether it's internal division or external division, our tool handles complex calculations for students, educators, and professionals exploring coordinate geometry concepts.
Formula:
The Section Formula is a fundamental theorem in coordinate geometry used to find the coordinates of a point P(x,y) that divides a line segment joining two distinct points A(x₁, y₁) and B(x₂, y₂) in a specific ratio m:n.
- Internal Division Formula: Point P lies between A and B.
P(x,y) = ((m·x₂ + n·x₁)/(m+n), (m·y₂ + n·y₁)/(m+n)) - External Division Formula: Point P lies outside the line segment AB, on the line containing AB.
P(x,y) = ((m·x₂ - n·x₁)/(m-n), (m·y₂ - n·y₁)/(m-n))
Where:
- (x₁, y₁): Coordinates of the first endpoint (Point A)
- (x₂, y₂): Coordinates of the second endpoint (Point B)
- m:n: The ratio in which the point P divides the line segment AB