Question

5. Prove that :
(i) AC – BC = B – A
(ii) BC - AC = A-B.​

Answer 1

Answer:

a. Proof: If a<b and c > 0, then, by definition, b−a > 0 and c > 0. But the product of any two positive numbers is positive, so bc− ac = c(b − a) > 0, which implies ac < bc. On the other hand, the product of a positive number and a negative number is a negative number. ... If 0 <a<b, then 1 b < 1 a .

b. For the other direction, the converse, we must prove that if |AC| = |AB| + |BC|, then the points are collinear and B is between A and C. First, the points must be collinear, for if they were not, then ABC would be a triangle and the triangle inequality would be true.