Question :

Find the mass and center of gravity of the lamina with density delta(x,y)=xy, lying in the first quadrant and bounded by the circle x^2 + y^2 = a^2 and the coordinates axes.

The book said that

" the center of gravity will be the same for x and y due to the symmetry of the figure. so y bar = x bar. "

I don't understand it. Could you please explain to me? Thank you very much.