# Problem when calculating the center of mass of a triangle

## Homework Statement

if the black dot is assumed by (0,0).find the center of mass coordinate of this triangle [/B]
i'm sorry but since the pic wont show ill attach the link here
https://ibb.co/4Ptw5T7 ## Homework Equations

centroid is 2/3 of median [/B]

## The Attempt at a Solution

the problem is when i try solve this problem by both method it always give me different answer first I'll use the 2/3 theorem first
~ by seeing the picture it shows us that the length of EF is 2√2(2/sin45) and length from D to midpoint(H) is √2 ,[/B]
EH √2 then the length of center of mass from point D, ⅔DH or ⅔√2 from here i turn this into x axis by multiply it by cos 45(since 90 on point D split into half) so i get ⅔√2.½√2 it become ⅔ this is the length from right side (point D) but the problem demand it from left side (black point) so it become 2-⅔=4/3(x axis)
for y axis is using same method and it will give also 4/3result
~and the second method is using vector addition and have form like (x1m1+x2m2)/(m1+m2) in my case (x1l1+x2l2)/(l1+l2) since it doesnt show any mass and just length , and im sure most you already know about this method
so ill straight to my attempt
for x axis (x1l1+x2l2+x3l3)/(l1+l2+l3)
where 1= ED 2=EF 3=DF
(1.2+1.2√2+2.2)/(2+2√2+2)=1.292
and exact same method for y axis
and give same result, and from here the problem is arises , now if we take a look 1.292 is length from left side to right (from black point 0,0) so it length from point D is 2-1.292=½√2 so for y axis it length from point D is 2-1.292=½√2 then if we use phytagorean theorem on both result we should able to determine the length from point D to the centrium ( i already calculated it on method 1) so it turned out like this √((½√2)²+(½√2)²)=1 and the answer should be ⅔√2 and if we try further more the length from D to mid point is 1/(2/3)=1,5 and how can there become 1,5??
sorry if i use weird term since im not native english speaker so i'm not familiar with it i , ill really glad if someone can explain this to me since both formula is valid at least so i think

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Do you know where the center of mass of any triangle should be at, just with basic geometry?

haruspex
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since it doesnt show any mass and just length
There's the problem. Lengths are not areas.

Do you know where the center of mass of any triangle should be at, just with basic geometry?
Do you know where the center of mass of any triangle should be at, just with basic geometry?
i don't say any type of triangle. if you open the link you will see it only ordinary triangle

i don't say any type of triangle. if you open the link you will see it only ordinary triangle
Well, I mean this:
https://en.m.wikipedia.org/wiki/Triangle_center
It just seems like this problem isn’t that complicated. The medians can be considered as linear equations. Then solve the system.

For instance:
The median from point D to line EF is y=x

Well, I mean this:
https://en.m.wikipedia.org/wiki/Triangle_center
It just seems like this problem isn’t that complicated. The medians can be considered as linear equations. Then solve the system.

For instance:
The median from point D to line EF is y=x
yes it just when i try both method it doesn't display same result so it leave me restless since i think both are valid equation but i'm not sure about the second since so far in problem lIke this is always give either mass of area just like what haruspex stated above . frankly it first time i learn about center of mass so the density is always same and it basically give me the generic equation that also applicable to area and when i try to match it with my knowledge about triangle centrium it just give more contradiction . but it also perhaps caused by my shallowness and mistakes, so if i the one that make mistake please show me the right things to do but if both method really doesn't show same result then I'm not in the position to talking about it