Center Proof

Center of Gravity Proof?

The “center of gravity” of the triangle with vertices at A, B, and C is the point 1/3(A+B+C). Show that the center of gravity of a triangle is always the same as that of the triangle formed by the midpoints of its sides.

What are the midpoints? They are:

M = (A+B)/2
N = (B+C)/2
O = (A+C)/2

If you plug that into the formula, you get:

1/3(M+N+O) = 1/3( (A+B)/2 + (B+C)/2 + (A+C)/2 ) = 1/3(A+B+C)

QED

HP Disaster Proof Data Center

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