Find the Center of Mass of the Rectangular Lamina with Vertices

Multiple Choice

Find the center of mass of the rectangular lamina with vertices $( 0,0 ) , ( 14,0 ) , ( 0,12 )$ , and $( 14,12 )$ for the density $\rho = k \left( x ^ { 2 } + y ^ { 2 } \right)$

A) $\left( 0 , \frac { 1533 } { 170 } \right)$
B) $\left( \frac { 1236 } { 85 } , \frac { 1533 } { 85 } \right)$
C) $\left( \frac { 618 } { 85 } , \frac { 1533 } { 170 } \right)$
D) $\left( \frac { 1533 } { 85 } , \frac { 1236 } { 85 } \right)$
E) $\left( \frac { 1533 } { 170 } , \frac { 618 } { 85 } \right)$