Malorie's blog

4-3 Symmetry


x-axis: 1. plug in (-y)
2.simplify
3.if equations are = then it has symmetry.

y-axis: 1. plug in (-x)
2. same as first
3. same as first


origin: 1. plug in (-x) and (-y)
2. same as first
3. same as first

y=x: 1. switch x and y
2. solve for y
3. same as first

Ex:
y^2+xy=10, for symmetry about the x-axis, y-axis, origin, and y=x.

x-axis: (-y)^2+x(-y)=10
y^2-xy=10
nooooooo!

y-axis: y^2+(-x)y=10
y^2-xy=10
noooopee!

origin: (-y)^2+(-x)(-y)=10
y^2+xy=10
YEEEEES (:

y=x: x^2+xy=10
Noooo shot

so the final answer would be that only the origin has symmetry to the beginning equation