Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Section 1.9 - The Coordinate Plane; Graphs of Equations; Circles - 1.9 Exercises - Page 106: 126

Answer

$$S(3,4)$$

Work Step by Step

We have the following points: $P(0,3)$ $Q(2,2)$ $R(5,3)$ $S(x,y)$ According to the definition of a parallelogram, its diagonals intercept each other at the midpoint of each of them. Using the midpoint formula $(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$, we can calculate the midpoint $M$ using either the diagonal $PR$ or the diagonal $QS$. $M_{PR}=(\frac{0+5}{2}, \frac{3+3}{2})=(2.5, 3)$ $M_{QS} = (\frac{2+x}{2}, \frac{2+y}{2})$ We also know, that these midpoints are on the same point $(M_{PR}=M_{QS})$. Which means: $\frac{2+x}{2}=2.5$ $2+x=5$ $x=3$ $\frac{2+y}{2}=3$ $2+y=6$ $y=4$ We have found point $S(3,4)$
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