(a) You may recall that for a triangle (not necessarily equilateral or right), there is a point called the centroid, the intersection of its medians. Place a general triangle on Cartesian coordinates, and find the coordinates of its centroid. Is the centroid equal to the centre of mass of three identical point masses placed at the vertices of the triangle? Show why or why not. (b) What is then, in vector notation, the appropriate generalisation of the centroid (also known as centre of mass/weight in many other languages) for all polygons?

(a) You may recall that for a triangle (not necessarily equilateral or right), there is a point called the centroid, the intersection of its medians. Place a general triangle on Cartesian coordinates, and find the coordinates of its centroid. Is the centroid equal to the centre of mass of three identical point masses placed at the vertices of the triangle? Show why or why not. (b) What is then, in vector notation, the appropriate generalisation of the centroid (also known as centre of mass/weight in many other languages) for all polygons?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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