This leschild will certainly teach you how to test for symmeattempt. You have the right to test the graph of a relation for symmetry via respect to the x-axis, y-axis, and also the origin. In this lesson, we will certainly confirm symmetry algebraically.

You are watching: Symmetric with respect to the origin examples

## Test for symmeattempt via respect to the x-axis.

**The graph of a relation is symmetric with respect to the x-axis if for eextremely point (x,y) on the graph, the suggest (x, -y) is likewise on the graph. To inspect for symmetry via respect to the x-axis, simply replace y through -y and also see if you still acquire the very same equation. If you execute obtain the very same equation, then the graph is symmetric with respect to the x-axis.**

**Example #1:****is x = 3y4 - 2 symmetric with respect to the x-axis?Rearea y through -y in the equation.X = 3(-y)4 - 2X = 3y4 - 2 **

**Since replacing y through -y offers the exact same equation, the equation x = 3y4 - 2 is symmetric through respect to the x-axis. **

## Test for symmetry with respect to the y-axis.

The graph of a relation is symmetric through respect to the y-axis if for eextremely point (x,y) on the graph, the allude (-x, y) is also on the graph.To check for symmeattempt with respect to the y-axis, simply replace x via -x and see if you still gain the very same equation. If you execute acquire the exact same equation, then the graph is symmetric through respect to the y-axis.

**Example #2:****is y = 5x2 + 4 symmetric via respect to the x-axis?Replace x with -x in the equation.Y = 5(-x)2 + 4Y = 5x2 + 4 **

**Since replacing x through -x offers the very same equation, the equation y = 5x2 + 4 is symmetric via respect to the y-axis. **

**Test for symmeattempt through respect to the beginning.**

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**The graph of a relation is symmetric through respect to the origin if for eextremely point (x,y) on the graph, the point (-x, -y) is likewise on the graph.To examine for symmeattempt with respect to the origin, just rearea x via -x and y via -y and see if you still obtain the very same equation. If you execute get the exact same equation, then the graph is symmetric via respect to the beginning.**

**Example #3:**is 2xy = 12 symmetric with respect to the origin?Replace x with -x and also y through -y in the equation.2(-x × -y) = 122xy = 12Due to the fact that replacing x via -x and also y via -y provides the very same equation, the equation 2xy = 12 is symmetric through respect to the beginning.

Everypoint you need to prepare for an important exam! K-12 tests, GED math test, fundamental math tests, geomeattempt tests, algebra tests.

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