a/b = c/d, |a| + |b| = |c| + |d|

[sspiegel]

this is from the DS problem "go the distance". Can someone help me prove that this is the case?

given,
a/b = c/d

and
|a| + |b| = |c| + |d|

Can someone provide the mathematical proof for a = c and b = d. The explanation just said it is, and I can see it intuitively, but can't prove it.

thanks,

[tim]

sure. whatever multiple c is of a (call it k), d is the same multiple of b. so c = ka and d = kb. now |c| + |d| = |ka| + |kb|, which can only happen if k = 1. so c = 1*a and d = 1*b