/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 120 Given an equation in \(x\) and \... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 120

Given an equation in \(x\) and \(y,\) how do you determine if its graph is symmetric with respect to the origin?

Short Answer

Expert verified
To determine if a given equation in \(x\) and \(y\) is symmetric with respect to the origin, a check is made to see if the equation remains the same when both \(x\) and \(y\) are replaced by their negatives \(-x\) and \(-y\). If it does, then it is symmetric about the origin.

Step by step solution

01

Understand Symmetry About The Origin

A graph is said to be symmetric about the origin, if rotating it by 180 degrees about the origin leaves the graph unchanged. Meaning, replace every point \((x, y)\) in the graph with point \((-x, -y)\) and the graph remains unchanged.
02

Apply The Test For Symmetry About The Origin

Assign the given equation and replace \(x\) by \(-x\) and \(y\) by \(-y\). If the resultant equation is equivalent to the original equation, it is symmetric about the origin.
03

Verify The Symmetry

Check if the transformed equation (after substituting \(x\) with \(-x\) and \(y\) with \(-y\)) is the same as the original equation. If they match, then the graph is symmetrical about the origin.

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