Precalculus (10th Edition)

Published by Pearson

Chapter 1 - Graphs - 1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry - 1.2 Assess Your Understanding - Page 17: 38

Answer

a) The point symmetric with respect to the x-axis is the point itself $(4,0)$ b) The point symmetric with respect to the y-axis is $(-4,0)$ c) The point symmetric with respect to the origin is also $(-4,0)$

Work Step by Step

The point on the graph is $(4,0)$ The symmetric points can be found on the graph by following the rules in the book: Symmetric with respect to the x-axis: if the point $(x,y)$ is on the graph then $(x,-y)$ is also on the graph. Symmetric with respect to the y-axis: if the point $(x,y)$ is on the graph then $(-x,y)$ is also on the graph. Symmetric with respect to the origin: if the point $(x,y)$ is on the graph then $(-x,-y)$ is also on the graph. Furthermore, the graph can be used as a proof of these statements. a) The point symmetric with respect to the x-axis is the point itself $(4,0)$ b) The point symmetric with respect to the y-axis is $(-4,0)$ c) The point symmetric with respect to the origin is also $(-4,0)$

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