The Center of Mass of a Lamina in the Shape $\rho ( x , y ) = 6 x + 3 y + 3$

Multiple Choice

The center of mass of a lamina in the shape of a region in the xy-plane bounded by the y-axis, y = x and y = 2 - x with area density $\rho ( x , y ) = 6 x + 3 y + 3$ is

A) $\left( \frac { 7 } { 8 } , \frac { 17 } { 16 } \right)$
B) $\left( \frac { 3 } { 8 } , \frac { 19 } { 16 } \right)$
C) $\left( \frac { 5 } { 8 } , \frac { 17 } { 16 } \right)$
D) $\left( \frac { 3 } { 8 } , \frac { 17 } { 16 } \right)$
E) $\left( \frac { 1 } { 8 } , \frac { 17 } { 16 } \right)$