(Geometry: point on line segment) Exercise 4.31 shows how to...

(Geometry: point on line segment) Exercise 4.31 shows how to test whether a point is on an unbounded line. Revise Exercise 4.31 to test whether a point is on a line segment. Write a program that prompts the user to enter the $x$ - and $y$ -coordinates for the three points $\mathrm{p} 0, \mathrm{p} 1,$ and $\mathrm{p} 2$ and displays whether $\mathrm{p} 2$ is on the line segment from p0 to p1. Here are some sample runs:

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Key Concepts

Collinearity

This concept determines whether three points lie on the same infinite line. In practice, you can check collinearity by verifying that the area of the triangle formed by the three points is zero or equivalently that the vector cross product of the vectors connecting the points is zero.

Line Segment

A line segment is a part of a line bounded by two distinct endpoints. Unlike an infinite line, a line segment has a fixed length and only includes the points between its endpoints, so testing whether a point lies on it requires additional constraints beyond checking if the point is collinear with the endpoints.

Bounding Box Check

Even if three points are collinear, the test point must also lie within the smallest rectangle (or bounding box) that contains both endpoints of the segment. This check ensures that the point is between the two endpoints rather than merely on the infinite line containing the segment.

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