Question

Sketch the region bounded by the curves, and visually estimate the location of the centroid. y = 2x, y = 0, x = 1 WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot Find the exact coordinates of the centroid.

Answer 1

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.

• to find centroid:

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 = $(\frac{a+c+e}{3} , \frac{b+d+f}{3} )$

• therefore , the exact coordinates of the centroid =

$(\frac{1+0+1}{3}, \frac{2+0+0}{3} ) = (\frac{2}{3}, \frac{2}{3} )$

this point is marked as G in the graph uploaded.