College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.1 - The Coordinate Plane - 1.1 Exercises - Page 92: 33


ABCD is a trapezoid. Area = $9$.

Work Step by Step

From the graph, the quadrilateral $ABCD$ has a pair of parallel sides, so $ABCD$ is a trapezoid. The area is $\displaystyle \frac{1}{2}$(sum of bases lengths)$\times$(height) $A=(\displaystyle \frac{b_{1}+b_{2}}{2})h$. $b_{1}=d(A, B)=\sqrt{(1-5)^{2}+(0-0)^{2}}=\sqrt{4^{2}}=4$. $b_{2}=d(C, D)=\sqrt{(4-2)^{2}+(3-3)^{2}}=\sqrt{2^{2}}=2$. The bases are parallel to the x-axis, so $h$ = difference in y-coordinates $= |3-0|=3$. Area = $(\displaystyle \frac{4+2}{2})3=9$.
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