Question

Analytically determine what type(s) of symmetry, if any, the graph of the equation would possess. Show your work.

Answer 1

We heva the following:

Two figures can be symmetric with respect to a point (central symmetry) or with respect to a line (axial symmetry).

In central symmetry, it is true that the distance of the symmetric points to the center of the symmetry is the same, and both are aligned with this center.

In axial symmetry, the distances of the symmetric points to the axis of symmetry is the same, and both are in the same perpendicular to said axis.

`x^2+y^2=3|x|`

grahp

Therefore, it has both symmetries.