Find the Center of Mass of a Lamina in the Shape

Multiple Choice

Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length $a = 15$ if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse. Assume the vertex opposite the hypotenuse is located at $( 0,0 )$ , and that the sides are along the positive axes.

A) $( 6,6 )$
B) $( 6,15 )$
C) $( 5,6 )$
D) $( 15,15 )$
E) None of these