Segment Addition Postulate Calculator

The segment addition postulate states that if point B is situated between points A and C on a straight line, then the lengths of the individual segments satisfy the linear equation AB + BC = AC. In coordinate geometry, the calculator also evaluates Euclidean distance squared relationships (such as AB^2 + BC^2 = AC^2 or variations depending on which point lies between the others) to verify whether three given points are strictly collinear.

Imagine you have a straight path divided into three sequential landmarks: A, B, and C. You know that the distance from point A to point B (Segment AB) measures 7 centimeters, and the distance from point B to point C (Segment BC) measures 12 centimeters. Applying the segment addition postulate equation, AB + BC = AC, you simply substitute your known values: 7 + 12 = AC. Therefore, the total length of Segment AC equals 19 centimeters. If you were testing for collinearity, the calculator matches these segment sums against coordinate squared distances to ensure the points form a single straight line.

Always verify the relative positions of your points before applying addition or subtraction. Ensure that the middle point actually lies directly between the two endpoints, otherwise the simple linear addition rule may not apply. When working with coordinate points rather than pre-measured lengths, double-check your sign conventions and decimal entries to maintain absolute precision.