Question 174515
</pre><font size=4><b>(0,10), (4,0), and (8,14).
Okay, we need to find the centroid of the triangular top where you can put the support to a point where it will be stable or balance.
We find the "x" & "y" coordinates of the cemtroid via--->{{{T[c]=(x[1]+x[2]+x[3])/3=(y[1]+y[2]+y[3])/3)}}},  working eqn
.
x-coordinates:
{{{T[c]=(0+4+8)/3=12/3=highlight(4=x)}}}
y-coordinates:
{{{T[c]=(10+0+14)/3=24/3=highlight(8=y)}}}
So, you put the post on point (4,8), as you see below:
{{{drawing(400,400,-3,12,-3,16,graph(400,400,-3,12,-3,16),triangle(0,10,4,0,8,14))}}}
With the Centroid where to put the support:
{{{drawing(400,400,-3,12,-3,16,graph(400,400,-3,12,-3,16),triangle(0,10,4,0,8,14),red(circle(4,8,.05)),red(circle(4,8,.08)),red(circle(4,8,.10)),red(circle(4,8,.12)),green(line(0,10,4,8)),green(line(4,0,4,8)),green(line(8,14,4,8)),red(circle(4,8.16)),red(circle(4,8,.19)))}}}


Thank you,
Jojo</pre>