Thread: Shrink numbers within a range preserving distance ratio

I am not sure whether this problem would belong to Algebra or set Theory, hopefully it belongs here... I am not a mathematician, so its hard for me to come to a concrete category. I am trying to solve a problem at hand, and I need to get this necessary step done in order to find a complete solution.


Problem Description:
Suppose I have some points spread (unequally) on a line within some range. I want to shrink the points within a smaller range, so that the old distance ratio between points remain preserved.

e.g.

I have points a,b,c,d,e,f,g spread between Range X & Y

X = 0.25 Y = 0.90
a = 0.25 , b=0.32 , c=0.45, , d=0.50, e=0.60, f=0.80, , g=0.90

As we can see above that the distances are uneuqal between the spreaded points. Now, I want to shrink these points to a smaller range X' & Y',

where
X' = 0.35 Y' = 0.65

How would I calculate values of a',b',c',d',e',f',g' , such that the distance ration between all these points remain same for the smaller range.

a' = ? , b'=? , c'=?, , d'=?, e'=?, f'=?, , g'=?

I have been trying to come up with a formula that would help me solve this problem, but am unable to formulate one.

I hope someone here can help me.

A simple way to do that is to regard the points as fractions of your original interval.

Call and the 'ratio to the interval' your new coordinates will then be

Originally Posted by brouwer

A simple way to do that is to regard the points as fractions of your original interval.

Call and the 'ratio to the interval' your new coordinates will then be

Thanks alot... I think this solution would work perfectly for me...