Answer to Question #186240 in Differential Geometry | Topology for Jethro

Question

Find the centroid of the area bounded by

x + 2y = 6, x= 0 y= 0

Answer 1

$Solution: Solve ~the ~ line ~x=0,y=0 ~ and ~ x+2y=6~by ~ taking ~ two ~ at ~ a ~time. \\We ~ get ~ the ~ vertices ~ of ~ triangle ~ as ~ (0,0),(6,0)~ and ~ (0,3). \\So ~we~get ~right ~ angled ~traiangle ~ as ~area. \\Hence ~ the ~ centroid ~ of ~ the ~triangle~ area ~is \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})=(\frac{0+6+0}{3},\frac{0+0+3}{3})=(\frac{6}{3},\frac{3}{3})=(2,1) \\\therefore~the ~centroid~ of~ the ~area ~bounded ~by~ x + 2y = 6, x= 0~ and~ y= 0 ~is~(2,1).$