Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 12 - Matrices - 12-6 Vectors - Lesson Check: 2

Answer

$$\langle9,-11\rangle$$

Work Step by Step

$\vec{RS}$ is the vector from point $R:(-2,5)$ to $S:(2,-8).$ The change in the x-direction is $$2-(-2)=4.$$ The change in the y-direction is $$-8-5=-13.$$ So the vector can be written in component form as $$\vec{RS}=\langle4,-13\rangle.$$ $\vec{PQ}$ is the vector from point $P:(-2,2)$ to $Q:(3,4).$ The change in the x-direction is $$3-(-2)=5.$$ The change in the y-direction is $$4-2=2.$$ So the vector can be written in component form as $$\vec{PQ}=\langle5,2\rangle.$$ To get the sum of two vectors, add components. $$\vec{RS}+\vec{PQ}=\langle4,-13\rangle+\langle5,2\rangle=\langle9,-11\rangle$$
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