Questions on Geometry: Triangles answered by real tutors!

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Question 150643: if (2,4) is the location of the centroid of a triangle. which CANNOT be the coordinates of the verticles of the triangle?
F= (0,0),(0,6),(6,6)
G=(3,4),(3,-2),(0,6)
H= (3,-2),(1,6),(2,8)
J= (2,0) ,(1,8),(3,4): if (2,4) is the location of the centroid of a triangle. which CANNOT be the coordinates of the verticles of the triangle?
F= (0,0),(0,6),(6,6)
G=(3,4),(3,-2),(0,6)
H= (3,-2),(1,6),(2,8)
J= (2,0) ,(1,8),(3,4)
Answer by Fombitz(1741) About Me  (Show Source):
You can put this solution on YOUR website!
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).