# Symmetry of a planar system and product of inertia

I read the following sentence here:

"The products of inertia occupy the off-diagonal positions and measure the asymmetry of the mass distribution with respect to the planes of the inertia frame of resolution. The greater the asymmetry about a plane, the larger the products of inertia associated with any axis in that plane."

If I have a planar system (3 red points):

the product of inertia $$I_{xy}=0$$, thus the above sentence is false because in my system there are not axes of symmetry, but the product of inertia is zero.

Moreover, the xy plane cannot be a plane of symmetry because the defition say that the masses should be out of the plane of symmetry.

Is this right? If no, can you explain me the above sentence with an example please?

Thank you so much.

• I think the planes of inertia are supposed to be going through the center of mass of the system, otherwise the sentence does not make sense (as you discovered) – Andrei Feb 4 at 3:34