Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

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.2 Graphs of Equations in Two Variables; Intercepts; Symmetry - F.2 Assess Your Understanding - Page 17: 30

Answer

(a) The symmetric point with respect to the x-axis for $(4,-2)$ is $(4,2)$. (b) The symmetric point with respect to the y-axis for $(4,-2)$ is $(-4,-2)$. (c) The symmetric point with respect to the origin for $(4,-2)$ is $(-4,2)$. Refer to the plot below.
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Work Step by Step

The point that is symmetric to the given point with respect to the $x$-axis can be reached by changing the coordinate from $(x,y)$ to $(x,-y)$: The symmetric point with respect to the $x$-axis for $(4,-2)$ is $(4,2)$. The point that is symmetric to the given point with respect to the $y$-axis can be reached by changing the coordinate from $(x,y)$ to $(-x,y)$: The symmetric point with respect to the $y$-axis for $(4,-2)$ is $(-4,-2)$. The point that is symmetric to the given point with respect to the origin can be reached by changing the coordinate from $(x,y)$ to $(-x,-y)$: The symmetric point with respect to the origin for $(4,-2)$ is $(-4,2)$.
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