Because the ratio of AB to BC is 3 to 5, we can take our unit of measurement to such that ABis3 and BCis5. Let C be some other point in the plane and let "x" be the distance from A to C. C can lie anywhere on the circle of radius 5 with center B. That circle crosses the line through A and B twice- and those mark the shortest and longest possible distance from B to C. When the circle crosses the line on the other side of B from A, the distance from B to C is 5- 3= 2 and when it crosses the line on the other side of A from B, the distance from B to C is 5+ 3= 8. The ratio of AB to AC must be between 3/8 and 3/2.