Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.1 Real Numbers, Functions, and Graphs - Exercises - Page 10: 38

Answer

Distance 5 from origin: (5,0), (-5,0), (0,5), (0,-5), (-3, 4), (3, 4), (-4, 3), (4,3), (-4, -3) , (-3, -4), (3,-4), (4, -3) Distance 5 from (2,3): (7,3), (-3,3), (2,8), (2,-2), (5, -1), (6, 0), (6, 6), (5, 7), (-1,7), (-2,6), (-2,0), (-1, -1)

Work Step by Step

To solve the distance 5 from the origin, you must think of the x-y plane. One way of viewing the problem is by visualizing the distance of '5' as the radius of a circle with center in the origin. If you picture the problem in this manner, any pair of points that lie on the circle's radius has distance 5 from the origin, all you must look for coordinates of the circle where both the x and y values are integers. In that case, your graph would look like the image attached. The same can be done for the second part of the problem, only that the center of the circle is now at (2,3) instead of (0,0) - graph also attached.
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