Question

Three points lie on the same straight line. If each point can act as an endpoint, how many distinct line segments can be formed using the set of points?

Answer 1

Assume that the points are A, B, and C, B is between A and C, and note that a distinct line segment means that, at most, one point can intersect. This means that if we have AB and AC, AB has more than one point and AB is part of AC, so they are not two distinct lines. However, AB and BC are distinct due to that they only intersect at B. Our options to connect points are AB, AC, and BC. Since AC overlaps BC and AB, if AC is used, we have 1 as our answer. However, we can use AB and BC, increasing our limit to 2.


 Look at the picture for a visual (B is the black, and A and C can be interchangeable with the other points), and feel free to ask further questions!