# Mass Point Geometry Confusion

1. Oct 15, 2011

### Quietus

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 $\cap$ 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.