The distance from a to b is actually |b - a| - the absolute value of numbers actually is defined as a distance!
For the sake of brevity, we'll assume that all the numbers here are positive. In this case, |b - a| = b - a. If we were to consider that some numbers are negative, establishing whether |b - a| is b - a or -(b - a) would take up too much time.
So you know that:
1. The distance between a and b will be |b - a| = b - a.
The distance between d and b will be |d - b| = d - b.
b - a = (d - b)/4
4b - 4a = d - b
5b - 4a = d
2. c - a = 3(d - c)
c - a = 3d - 3c
4c - a = 3d
(4c - a)/3 = d
Combine the last things to get: (4c - a)/3 = 5b - 4a, which means that 4c - a = 15b - 12a. Subtract 3a from each side to get 4c - 4a = 15b - 15a
4c - 4a = 15b - 15a
4(c - a) = 15(b - a)
(b - a)/(c - a) = 4/15
Edit: I realized that I mixed up the second stmt.
Last edited by
DanaJ on Fri May 29, 2009 11:03 pm, edited 1 time in total.
