The Center of Mass of a Lamina in the Shape $3 x + 2 y = 18$

Multiple Choice

The center of mass of a lamina in the shape of a region in the xy-plane bounded by the y-axis, $3 x + 2 y = 18$ and y = 0 with area density $\rho ( x , y ) = x y$ is

A) $\left( \frac { 27 } { 2 } , \frac { 81 } { 5 } \right)$
B) $\left( \frac { 12 } { 5 } , \frac { 18 } { 5 } \right)$
C) $\left( \frac { 3 ( 2 + \pi ) } { 32 } , \frac { 3 ( 2 + \pi ) } { 32 } \right)$
D) $\left( \frac { 3 } { 8 } , \frac { 17 } { 16 } \right)$
E) $\left( \frac { 35 } { 22 } , \frac { 102 } { 77 } \right)$