Find the coordinates of the centroid G of the triangular region with vertices (0,0),(a,0),(b,c).
for the centroid x = (1 / area) * double integral ( x dA)
y = (1 / area) * double integral ( y dA)
The Attempt at a Solution
Ok, what i did so far for this was try to get an equation for the lines on the left and right of the triangle. i got x = by/c and x = -y(a-b)/c + a (both were found using point slope)
Then I integrated with respects to x first and used the above equations as my limits of integration, and then integrated with respects to y and used 0 and c as limits of integration.
I want to know if that sounds like the right method of going into this problem. I get a really long mess of a's and b's for x and c canceled out. It feels like I'm missing something.
The whole point of the assignment was to try to prove that the three medians of a triangle intersect the centroid, but if I'm already going in the right direction, I'm sure I can figure the rest out.