Ratios of Directed Line Segments Calculator

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Choose whether to find point P given a ratio, or find the ratio given three collinear points.
Internal division places P between A and B. External division places P on the line through A and B but outside the segment.
The x-coordinate of the starting point A.
The y-coordinate of the starting point A.
The x-coordinate of the terminal point B.
The y-coordinate of the terminal point B.
The first part of the ratio m:n (portion from A to P).
The second part of the ratio m:n (portion from P to B).
P: x-coordinate
2.2

The x-coordinate of the partitioning point P.

P: y-coordinate3.6
Ratio m2
Ratio n3
Ratio m:n0 : 0
Segment AB length5
AP length2
PB length3
Division typeInternal division
AP length2
PB length3
AB total length5

P = (2.2000, 3.6000) - Internal division in ratio 0 : 0

  • AP = 2.0000 units, PB = 3.0000 units, confirming a internal division in ratio 0 : 0.
  • The full segment AB has length 5.0000 units.
  • The section formula works for any ratio of positive real numbers. Use external division when the ratio is applied beyond the endpoint B.

Next stepThe midpoint of this segment is (2.5000, 4.0000). To trisect the segment, compute P with ratios 1:2 and 2:1.

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