P is an arbitary point , and p = A P A C . ...

Ayanna Trujillo

Ayanna Trujillo

Answered

2022-06-25

P is an arbitary point , and p = A P A C .   x = A X A M , where AM is a median. Observe that x = 2 3 when p = 1 2 . Find a general formula for x in terms of p.

Answer & Explanation

Cristian Hamilton

Cristian Hamilton

Expert

2022-06-26Added 23 answers

Step 1
If you put two unit masses at B and C and a mass m at A, then you can find the center of mass in two different ways:
1) put a mass of 2 at M (which is the center of mass of B and C) and then find X as the center of mass between M and A, so that A X : X M = m : 2 ;
2) put a mass m + 1 at the center of mass of A and C and then find X as the center of mass between P and B; this can work only if the center of mass of A and C is at point P, so that A P : P C = m : 1 .
From these two relations you can eliminate m and find x as a function of p.

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