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# finding the expression of the centroid watch

1. hello again,

thanks for any help (and sorry I don't yet have latex)

A,B,C are points in an Argand diagram representing the complex numbers a,b,c. M is the mid-point of AB and G is the point dividing the median CM in the ratio 2:1. Show that G represents the number (a+b+c)/3

work done: GC/GM = 1/2 => (c-g)/(g-m) = 1/2 => 2(c-g) = g-m =>
3g = 2c+m

but I can't obtain the result that 2c + m. I think it may help using the fact that m is the midpoint of a and b (as i haven't yet used it) though simply substituting (a-b)/2 for m doesn't do it.

that's all ive thought of...
2. Latex help
http://www.thestudentroom.co.uk/wiki/LaTex
3. The question's a little ambiguous, but I would take it as meaning that c-g = 2(g-m), which gets the answer, on the basis of CM meaning C to M, and the two being first in 2:1. Also note that m isn't (a-b)/2. Think of a-b as the line from B to A, so (a-b)/2 is the line from B to M, whereas you want the line from the origin to M to be m.
4. thank you

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