Question 150643
The equation for the centroid of a triangle using the vertices coordinates is,
({{{x[c]}}},{{{y[c]}}})=({{{(1/3)(x[1]+x[2]+x[3])}}},{{{(1/3)(y[1]+y[2]+y[3])}}})
or the coordinates must make,
{{{(1/3)(x[1]+x[2]+x[3])=2}}}
{{{(1/3)(y[1]+y[2]+y[3])=4}}}
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Let's look at each case,
F= (0,0),(0,6),(6,6)
x:{{{(1/3)(0+0+6)=2}}}
y:{{{(1/3)(0+6+6)=4}}}
Set F can be the coordinates, they match the centroid coordinates(2,4).
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G=(3,4),(3,-2),(0,6)
x:{{{(1/3)(3+3+0)=2}}}
y:{{{(1/3)(4-2+6)=8/3}}}
Set G cannot be the coordinates, they do not match the centroid coordinates(2,4).
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Let's verify the other two.
H= (3,-2),(1,6),(2,8)
x:{{{(1/3)(3+1+2)=2}}}
y:{{{(1/3)(-2+6+8)=4}}}
Set H can be the coordinates, they match the centroid coordinates(2,4).
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J= (2,0) ,(1,8),(3,4)
x:{{{(1/3)(2+1+3)=2}}}
y:{{{(1/3)(0+8+4)=4}}}
Set J can be the coordinates, they match the centroid coordinates(2,4).