- #1

John004

- 37

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## Homework Statement

1. Show that for an arbitrary uniform triangle ABC, with A at (x

_{1}, y

_{1}), B at (x

_{2},y

_{2}), C at (x

_{3}, y

_{3}), the CM (x

_{cm}, y

_{cm}), is simply defined by x

_{cm}=(x

_{1}+x

_{2}+x

_{3})/3, and y

_{cm}=(y

_{1}+y

_{2}+y

_{3})/3

## Homework Equations

x

_{cm}= 1/M * ∫xdm

y

_{cm}= 1/M * ∫ydm

M = ∫dm = ∫δdA where δ = M/A = dm/dA

for uniform mass distribution

M = δ∫dA

## The Attempt at a Solution

I'm not really too sure on how to set up the triangle for this problem. My professor had a picture of an arbitrary triangle with the vertices at the specified coordinates. Would it be alright to place my origin with the longest side of the triangle lying on the x-axis and then both end points of that side connect to a point on the y-axis? The coordinates of the vertices from left to right would then be (x

_{1},0), (0,y

_{2}), and (x

_{3}, 0). Would this defeat the purpose of the exercise? I'm pretty lost here.