Question 149652
The centroid of a triangle with vertices at ({{{x[a]}}},{{{y[a]}}}),({{{x[b]}}},{{{y[b]}}}),({{{x[c]}}},{{{y[c]}}}) is equal to
({{{X}}},{{{Y}}})={{{(1/3)}}}({{{x[a]+x[b]+x[c]}}},{{{y[a]+y[b]+y[c]}}})
In the first case,
({{{X}}},{{{Y}}})={{{(1/3)}}}({{{a+b+c}}},{{{p+q+r}}})
In the second case,
({{{X}}},{{{Y}}})={{{(1/3)}}}({{{-1-2+3}}},{{{5+8+3}}})
({{{X}}},{{{Y}}})={{{(1/3)}}}({{{0}}},{{{16}}})
({{{X}}},{{{Y}}})=({{{0}}},{{{16/3}}})
{{{drawing( 300, 300, -4, 4, -2, 10,grid( 1 ),blue(circle( 0, 5.333, .12 )),
green(line( -1, 5, -2, 8)),
green(line( -2, 8, 3, 3)),
green(line( 3, 3, -1, 5))
)}}}