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M2

How do I prove that the centroid is at the position of the mean of the vertices of a triangle?


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Original post by anoymous1111
How do I prove that the centroid is at the position of the mean of the vertices of a triangle?


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I guess by centroid you mean "centre of mass", as opposed to its meaning of "intersection of the medians of a triangle"

1. It's easy to show that the centre of mass must lie on the medians of the triangle, so convince yourself of this first.

2. Find vector equations describing the medians of the triangle, then show that they a) intersect at a common point and b) this common point lies 2/3 of the way from the vertices along the medians.
Reply 2
The proof is done in the M3 book by calculus. I don't think you'll be expected to know the proof for M2.
Original post by aymanzayedmannan
The proof is done in the M3 book by calculus. I don't think you'll be expected to know the proof for M2.


Oh ok that's good then! Thank you!


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