Answer
$(0,0)$ and $(8,0)$.
Work Step by Step
Let the point(s) be $(x,0)$, its distance to $(4,-3)$ is $d=\sqrt {(x-4)^2+(0+3)^2}=5$ or $(x-4)^2=16$, thus $x=4\pm4=0,8$ which give answers $(0,0)$ and $(8,0)$.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter F - Foundations: A Prelude to Functions - Section F.1 The Distance and Midpoint Formulas - F.1 Assess Your Understanding - Page 7: 47
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