Centroid Question: Proving AM=2AG using Law of Centroids and (A,2),(B,1),(C,1)

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In summary, the problem is to show that AM=2AG, where M is the center of [BC] and N is the centroid of the points (A,2) and (B,1). The attempt at a solution involved using a law to get the equation 4AG=2AM+0.5MB+0.5MC, but it is unclear what law was used and what G represents.
  • #1
mtayab1994
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Homework Statement



(A,2),(B,1),(C,1)

and M is the center of [BC] and N is the centroid of: (A,2) and (B,1)

Homework Equations



show that AM=2AG

The Attempt at a Solution



I used the law and i got 4AG=2AM+0.5MB +0.5MC

But what did i do wrong?
 
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  • #2
mtayab1994 said:

Homework Statement



(A,2),(B,1),(C,1)
I have no idea what you mean by these ordered pairs.

What exactly is the problem you're trying to solve?
mtayab1994 said:
and M is the center of [BC] and N is the centroid of: (A,2) and (B,1)

Homework Equations



show that AM=2AG


The Attempt at a Solution



I used the law and i got 4AG=2AM+0.5MB +0.5MC
What law?
mtayab1994 said:
But what did i do wrong?
 
  • #3
And what is G?
 

FAQ: Centroid Question: Proving AM=2AG using Law of Centroids and (A,2),(B,1),(C,1)

What is a centroid?

A centroid is the geometric center of a shape or object. It is the point where all the mass of the object is evenly distributed.

How is a centroid calculated?

A centroid is typically calculated by finding the average of the x-coordinates and the average of the y-coordinates of all the points that make up the shape or object.

What is the significance of a centroid?

The centroid is an important concept in mathematics and physics. It is used to determine the center of mass of an object, which is crucial in calculating the object's stability and balance.

Can a centroid be outside of the shape?

Yes, a centroid can be outside of the shape if the shape is irregular or has holes. In these cases, the centroid may be located outside of the shape, but it still represents the center of mass of the object.

How is a centroid used in real-world applications?

The concept of centroids is used in various real-world applications, such as architecture, engineering, and physics. It is used to determine the stability of structures, the balance of vehicles, and the distribution of mass in various objects.

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