Question 1086073

x + y = 0
y = -x

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Check for y-axis symmetry: replace x with -x and simplify.  If it results in the original equation, then it is symmetrical about the y-axis:

y = -(-x) = x  —> NOT symmetrical about y-axis
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Check for x-axis symmetry: replace y with -y and simplify.   If it results in the original equation, then it is symmetrical about the x-axis:

-y = -x  —> y = x —> NOT symmetrical about x-axis

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Check for symmetry about the origin:  change x to -x, change y to -y, simplify.  If original equation pops out, then the curve is symmetrical about the origin:

-y = -(-x)  —>   y = -x  —>  YES, symmetrical about the origin.