Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.10 - Lines - 1.10 Exercises - Page 116: 96

Answer

Slopes have to be the same:$$m_a=m_b=m_c$$ If $A$ and $B$ are the furthest seats and $C$ is in between them. For the seats to be lined, the next equation must be fulfilled $$AB = AC+CB$$

Work Step by Step

Suppose we have $3$ points (three seats) $A, B$ and $C$. There can be at most $3$ possible lines connecting these points. Let's assume that these lines are $a, b$ and $c$ (And let $m$ be value of the slope). These points will be laying on the same line, if and only if $$m_a=m_b=m_c$$ In case of using the Distance Formula, let $A$ and $B$ be the furthest seats and $C$ be in between them. For the seats to be lined, the next equation must be fulfilled $$AB = AC+CB$$
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