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Mass Point Geometry Confusion

  1. Oct 15, 2011 #1
    Aaaagh. I'm really confused right now. I just started learning MPG a few hours ago so go easy on me. It's hard to explain in word but I'll try.

    Consider this:

    In ΔABC, D, E, and F are the trisection points of AB, BC, and CA nearer A, B, and C respectively.

    Let BF [itex]\cap[/itex] AE = J. Show that BJ:JF = 3:4 and AJ:JE = 6:1.

    Using my basic knowledge on MPG, this started out easy. I assigned the masses of A, B, and C to be 1, 4, and 2 respectively. A=1 since CF=1, C=2 since AF=2 and B=4 because (2/1)*C=4. Now using this, I figured out JF would be equal to the value of B which is 4. Thus the value of BJ must be 3 since (A+B+C)=7 and 7-4 = 3. This resulted in BJ:JF = 3:4. Pretty straightforward.

    This is where it got tricky. I knew that by using my previous values, I could come up with JE=1 and AJ=6 easily. Then this thought came to me. I could assign C=1, B=2, and A=4 just by using different reference points. This would result in a different ratio for AJ:JE.

    I must be doing something wrong. If someone here could please explain to me where I went wrong or why this is like this, I'd be very grateful.

    If my explanation was a bit confusing, I could explain it better if you asked questions.
  2. jcsd
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