Proving a 2:1 ratio triangle having a Zero Vector

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SUMMARY

The discussion centers on solving a geometry problem involving a triangle with a 2:1 ratio and a zero vector. The user, aeromat, presents their initial equations but struggles to incorporate the 2:1 ratio effectively. A suggestion is made to label the midpoints of each side as A, B, and C, and to utilize the vectors GA, GB, and GC in the equations to progress towards a solution.

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  • Familiarity with triangle properties and ratios
  • Knowledge of midpoint theorem in geometry
  • Basic proficiency in algebraic manipulation of equations
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  • Learn about the midpoint theorem and its implications in triangle geometry
  • Explore the concept of ratios in geometric figures
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aeromat
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Homework Statement


I need help once again with this question below:
62-17-p292.png


Thanks,
aeromat



The Attempt at a Solution



This is what I have so far:
GP = GQ + QP
GQ = GP + PQ
GR = GP + PR

GP + GQ + GR = GQ + QP[-] + PQ[+] + GP + PR + GP
GP + GQ + GR = GQ + 2GP + PR

I am stuck now. I took the approach of taking GP + GQ + GR individually and finding their vector components.
 
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you haven't used the 2:1 ratio fact anywhere. try using that.

hint: name the mid points of each side A,B,C. And try to use GA, GB, GC in your equations.
 

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