Chapter 7 · Question 3

How can the distance formula be used to test whether three points are collinear?

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Answer

Direct Answer

Find the three pairwise distances. If the sum of two smaller distances equals the largest distance, the points are collinear.

Simple Explanation

For points on one line, one point lies between the other two, so two distances add to the third.

Exam-Ready Structure

Given points A,B,CA,B,C, compute ABAB, BCBC, and ACAC. If AB+BC=ACAB+BC=AC or another similar sum holds, then the three points lie on a straight line. If no such relation holds, the points are not collinear.

Key Points

  • Find the three pairwise distances.