P is an arbitary point , and , where AM is a median. Observe that when . Find a general formula for x in terms of p.
Answer & Explanation
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 ; 2) put a mass 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 . From these two relations you can eliminate m and find x as a function of p.
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