Question 1086073: Algebraically determine if the relation x + y = 0 is symmetric with respect to the x-axis, y-axis, the origin or has no symmetry.
a.y-axis
b.x-axis
c.no symmetry
d.the origin
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website!
x + y = 0
y = -x
—
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
—
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
—
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.
|
|
|
