College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 2 - Section 2.1 - Rectangular Coordinates and Graphs - 2.1 Exercises - Page 179: 32



Work Step by Step

Let $(m,n)$ be the missing endpoint. Using $\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2} \right)$ or the Midpoint Formula, then the coordinates of the missing endpoint, given that the midpoint is $( -7,6 )$ and the other endpoint is $( -9,9 )$ are \begin{array}{l}\require{cancel} \dfrac{m-9}{2}=-7 \\\text{AND}\\ \dfrac{n+9}{2}=6 .\end{array} Solving these equations separately results to \begin{array}{l}\require{cancel} m-9=2(-7) \\\\ m-9=-14 \\\\ m=-14+9 \\\\ m=-5 \\\text{AND}\\ n+9=2(6) \\\\ n+9=12 \\\\ n=12-9 \\\\ n=3 .\end{array} Hence, the missing endpoint is $ (-5,3) .$
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