Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - 2.1 Rectangular Coordinates and Graphs - 2.1 Exercises - Page 193: 37

Answer

$$\color{blue}{(5,-4)}$$

Work Step by Step

To find the endpoint $B(x,y)$ when given the endpoint $A(19,16)$ and the midpoint $M(12,6)$ we will use the midpoint formula: $${(\frac{x_{a}+x_{b}}{2},\frac{y_{a}+y_{b}}{2})}=M$$ $${(\frac{19+x_{b}}{2},\frac{16+y_{b}}{2})}=(12,6)$$ To find the $x$ value of $B$: $\frac{19+x}{2}=12$ $19+x=24$ $x=5$ To find the $y$ value of $B$: $\frac{16+y}{2}=6$ $16+y=12$ $y=-4$ So, the endpoint is at: $$\color{blue}{(5,-4)}$$
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