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 104: 119

Answer

$(a)$ $(8,5)$ $(b)$ $(a+3, b+2)$ $(c)$ $(0, 2)$ $(d)$ $A(-5, -1)$ => $A'(-2, 1)$ $B(-3, 2)$ => $B'(0, 4)$ $C(2, 1)$ => $C'(5, 3)$

Work Step by Step

Shifting to the right means to increase $x$ value of a point by $3$ units. Shifting a point upward, means to increase $y$ value by $2$ units. $(a)$ The point $(5,3)$ will become $(5+3, 3+2)$ => $(8,5)$ $(b)$ Point $(a,b)$ will become $(a+3, b+2)$ $(c)$ To find the point which was shifted by these units, then we have to do the calculation backwards. Instead of increase we have to decrease the $x$ and $y$ values, so we will take the original values of the point. $(3,4)$ was $(3-3, 4-2)$ => $(0, 2)$ $(d)$ In this case we have to apply the same calculation to each of these points. $A(-5, -1)$ => $A'(-5+3, -1+2)$ => $A'(-2, 1)$ $B(-3, 2)$ => $B'(-3+3, 2+2)$ => $B'(0, 4)$ $C(2, 1)$ => $C'(2+3, 1+2)$ => $C'(5, 3)$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.