Weight
In modern scientific usage, weight and mass are fundamentally different quantities: mass is an intrinsic property of matter, whereas weight is a "force" that results from the action of gravity on matter: it measures how strongly the force of gravity pulls on that matter. However, in most practical everyday situations the word "weight" is used when, strictly, "mass" is meant. For example, most people would say that an object "weighs one kilogram", even though the kilogram is a unit of mass.
Mass point geometry
Solution. We may arbitrarily assign the mass of point formula_37 to be formula_38. By ratios of lengths, the masses at formula_39 and formula_40 must both be formula_41. By summing masses, the masses at formula_23 and formula_26 are both formula_44. Furthermore, the mass at formula_31 is formula_46, making the mass at formula_34 have to be formula_48 Therefore formula_35 formula_50 and formula_51. See diagram at right.