prove the location of the centroid

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tmd1979

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The medial triangle ABC is the triangle with vertices at the midpoints of the sides AB, AC, and BC of triangle ABC. From an arbitraty point O that is not a vertex of triangle ABC, prove the location of the centroid is given by (vector OA + vector OB + vector OC)/3.

I am stuck. The book I am using does not provide very many or very good examples in it. I am confused. :?

Please help if you could!

Thanks!
 
tmd1979 said:
The medial triangle ABC is the triangle with vertices at the midpoints of the sides AB, AC, and BC of triangle ABC. From an arbitraty point O that is not a vertex of triangle ABC, prove the location of the centroid is given by (vector OA + vector OB + vector OC)/3.

I am stuck. The book I am using does not provide very many or very good examples in it. I am confused. :?

Please help if you could!

Thanks!
Click to expand...

Do you know the process of locating the centroid of a triangle?

If the text-book does not help you - google the topic.Tell us what you found.

Please share your aork with us, indicating exactly where you are stuck - so that we may know where to begin to help you.
 
I understand that the (OA + OB)/2, (OB + OC)/2, and (OA+OC)/2. Here is what I am thinking:

[(OA+OB)/2 + (OB+OC)/2 + (OA+OC)/2]/3 = [OD+OE+OF]/3
[2(OA+OB+OC)]/3=[OD+OE+OF]/3
(1/3)(OA+OB+OC)=(1/3)(OD+OE+OF)

I don't know if these is even on the right track, let alone correct. Any advice you can give is appreciated!

Thanks and have a great night!
 
Subhotosh Khan said:
Please share your aork with us, indicating exactly where you are stuck - so that we may know where to begin to help you.
Click to expand...
Unforgivable spelling error: aork ; 42 minutes in the corner, NOW!
 
Denis,

That is concatination of arguements and work. I am trying to sprinkle my statements with copy-writable originalities.
 
Subhotosh Khan said:
Denis,
That is concatination of arguements and work. I am trying to sprinkle my statements with copy-writable originalities.
Click to expand...
Well ok then: make it 41 minutes :twisted:
 
tmd1979 said:
I understand that the (OA + OB)/2, (OB + OC)/2, and (OA+OC)/2. Here is what I am thinking:

[(OA+OB)/2 + (OB+OC)/2 + (OA+OC)/2]/3 = [OD+OE+OF]/3 <<< What theorem are you using to claim that?
[2(OA+OB+OC)]/3=[OD+OE+OF]/3 <<< Does not follow from above - where did it come from?
(1/3)(OA+OB+OC)=(1/3)(OD+OE+OF) <<< Does not follow from above - where did it come from?

I don't know if these is even on the right track, let alone correct. Any advice you can give is appreciated!

Thanks and have a great night!
Click to expand...
 
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