Find the Mass and the Center of Mass of the Lamina

Multiple Choice

Find the mass and the center of mass of the lamina occupying the region $R$ , where $R$ is the triangular region with vertices $( 0,0 ) , ( 5,2 )$ , and $( 10,0 )$ , and having the mass density $\rho ( x , y ) = x$ .

A) $m = 50 , ( \bar { x } , \bar { y } ) = \left( \frac { 2 } { 3 } , \frac { 35 } { 6 } \right)$
B) $m = 10 , ( \bar { x } , \bar { y } ) = \left( \frac { 2 } { 3 } , \frac { 35 } { 6 } \right)$
C) $m = 10 , ( \bar { x } , \bar { y } ) = \left( \frac { 35 } { 6 } , \frac { 2 } { 3 } \right)$
D) $m = 50 , ( \bar { x } , \bar { y } ) = \left( \frac { 35 } { 6 } , \frac { 2 } { 3 } \right)$