# Let A and B be two distinct points. (a) Prove that for each real number x Z -1 there exists a unique

Let A and B be two distinct points. (a) Prove that for each real number x Z _1 there exists a unique point X on ('AB such that AX/XB D x. (The fraction AX/XB is to be interpreted as a sensed ratio.) (b) Prove that there is no point X on ('AB for which AX/XB D _1. (c) Draw a graph that illustrates how AX/XB varies as the point X moves along the line ('AB .