Answer:
the graph is in the attachment.
the coordinates of the centroid : (2/3,2/3)
Step-by-step explanation:
- y=0 represents x-axis ( you can easily mark it on the graph)
- now draw x=1 line.( It is a line parallel to y axis and passing through the point (1,0) )
- y=2x is a line which passes through origin and has a slope "2"
by using these sketch the region.
I have uploaded the region bounded in the attachment. You may refer it. The region shaded with grey is the required region.
it can be easily identified that the formed region is a triangle
- the coordinates of three vertices of the triangle are
(1,2) , (0,0) , (1,0)
( See the graph. the three intersection points of the lines are the three vertices of the triangle)
- for general FORMULA, let the coordinates of three vertices of a triangle PQR be P(a,b) , Q(c,d) , R(e,f)
- then the coordinates of the centroid( let say , G) of the triangle is given by
G = [tex](\frac{a+c+e}{3} , \frac{b+d+f}{3} )[/tex]
- therefore , the exact coordinates of the centroid =
[tex](\frac{1+0+1}{3}, \frac{2+0+0}{3} ) = (\frac{2}{3}, \frac{2}{3} )[/tex]
this point is marked as G in the graph uploaded.
